A bibliography on spline functions

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Citation for published version (APA):

van Rooij, P. L. J., & Schurer, F. (1971). A bibliography on spline functions. (EUT report. WSK, Dept. of Mathematics and Computing Science; Vol. 71-WSK-02). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1971

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September 1971

Technological University Eindhoven

Netherlands

Department of Mathematics

A BIBLIOGRAPHY ON SPLINE FUNCTIONS

by

P.L.J. vanRooy and F. Schurer

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A bibliography on spline functions by

P.L.J. van Rooij and F. Schurer

T.H.-Report 71-WSK-02 October 1971

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Introduction

This bibliography aims to be a reference to the knowledge concerning the theory and application of spline functions. The main part consists of a list which is ordered chronologically and, for publications that have ap-peared in the same year, alphabetically. Moreover, there is an index of authors together with a coded list of the papers they have contributed to the field.

This compilation of spline literature includes three kinds of publica-tions, namely papers in mathematical periodicals, books and doctoral disser-tations, all of which have appeared before January l, 1971. We remark that a fourth kind of publication, reports, has been deleted from the bibliography. There are various reasons for this omission.

(i) There is a wide variety in the status and quality of reports. Some of them are meant only for internal use whereby the communicated results are occasionally not yet in their definite form. Moreover, what is really worthwhile will sooner or later be published in the current mathematical journals.

(ii) Although it would be relatively easy to give a long and impressive list of reports (one only needs to think of the large number of reports issued on the subject by the Mathematics Research Center at the Uni-versity of Wisconsin), it no doubt would be a formidable task to give a representative survey of the literature existing in this form. A good deal of these publications is hard to retrieve and the distribution is often very limited. Therefore, we do not feel qualified to make an at-tempt in this direction.

Besides this list, there are several other sources where one can find elaborate references to the literature on spline functions. In this respect we want to mention the bibliographies in the monograph of Ahlberg, Nilson and Walsh [67 - 2] and in the books edited respectively by Greville

[69 - 24] and Schoenberg [69 - 69]. Other useful information is cor1tained in the bibliography "Recent publications in approximation theory with emphasis on computer applications", compiled by C.L. Lawson (Computer Reviews

2.

(1968), 691-699). One may also consult the paper by Schultz and Varga [67 - 34 J.

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The journal abbreviations are those given in Mathematical Reviews 41 (1971), 1939-1960. We have strived to add to each paper one or more

ref-ereaeea to reviews in Mathematical Reviews (MR), Zentralblatt fur Mathematik (Zb), Computing Reviews (CR), Computer Abstracts (CA), Bulletin Signaletique 110 (BS) and DissertationJAbstracts (DA). An asterisk indicates that the publication is a doctoral dissertation or a book that is mainly concerned with spline functions.

The bibliography contains a total number of 368 items. The bulk of these books and papers, 311 or 85%, has been published during the years 1966-1970. This clearly shows the explosive growth of this part of approxi-mation theory. Although the bibliography is certainly not complete, we hope that it gives a reasonable survey of the existing literature on spline func-tion theory until January I, 1971.

During the project Miss Yvonne Naus of the mathematics library of the Technological University Eindhoven has been of valuable assistance to us. It

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3

-Bibliography

1904 1. Runge, C.

Theorie und Praxis der Reihen. § 20.

Goschen'sche Verlagshandlung, Leipzig, 1904.

1938

1. Quade, W.; Collatz, L.

Zur Interpolationstheorie der reellen periodischen Funktionen. S.-B. Preuss. Akad. Wiss. Phys.-Math. Kl. 30 (1938), 383-429.

(Zb ~' p. 397.)

1940

I. Favard, J.

Sur !'interpolation.

J. Math. Pures Appl. ~'no. 9 (1940), 281-306. (MR

l'

p. 114; Zb 23, p. 24.)

1941

I. Popoviciu, T.

Notes sur les fonctions convexes d'ordre superieur. IX. Bull. Math. Soc. Sci. Math. R.S. Roumanie 43 (1941), 85-141.

(MR ]_, p. 116.)

1942

I. Love, A.E.H.

A treatise on the mathematical theory of elasticity. § 262; p. !•04.

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1946

1. Schoenberg. I.J.

Contributions to the problem of approximation of equidistant data by analytic functions.

Part A: On the problem of smoothing of gradiation. A first class of analytic approximation formulae.

Quart. Appl. Math.

i

(1946), 45-99. (MR

l,

p. 487.) 2. Schoenberg, I.J.

Contributions to the problem of approximation of equidistant data by analytic functions.

Part B: On the problem of osculatory interpolation. A second class of analytic approximation formulae.

Quart. Appl. Math.

i

(1946), 112-141. (MR ~' p. 55.)

1949

1. Sard, A.

Best approximate integration formulas; best approximation formulas.

~

Amer. J. Math.

2!

(1949), 80-91. (MR

lQ,

p. 576; Zb 39. p. 341.) 2. Schoenberg, I.J.; Whitney, A.

Sur la positivite des determinants de translations des fonctions de frequence de Polya, avec une application

a

un probleme d'interpolation. C.R. Acad. Sci. Paris Ser. A 228 (1949), 1996-1998. (MR

!l'

p. 86.) 3. Synge, J.L.; Griffith, B.A.

Principles of mechanics. pp. 92-98. McGraw-Hill, New York, 1949.

1950 1. Meyers, L.F.; Sard, A.

Best approximate integration formulas.

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5

-2. Meyers, L.F.; Sard, A.

Best interpolation formulas.

J. Math. and Phys. 29 (1950), 198-206. (MR ~' p. 396; Zb 40, p. 28.)

1953 1. Schoenberg, I.J.; Whitney, A.

1.

On Polya frequency functions. III: The positivity of translation deter-minants with an application to the interpolation problem by spline curves.

Trans. Amer. Math. Soc. 74 (1953), 246-259. (MR .!!!_, p • 732.)

1956 Sokolnikoff, I.S.

Mathematical theory of elasticity. p. 1 • McGraw-Hill, New York, 1956.

1957 1. Holladay, J.C.

A smoothest curve approximation.

Math. Tables Aids Comput.

!l

(1957), 233-243. (MR 20, 414; Zb 84, p. 349.)

1958 1. Schoenberg, I.J.

Spline functions, convex curves and mechanical quadrature. Bull. Amer. Math. Soc. 64 (1958), 352-357. (MR 20, 7174; Zb 85, p. 337.)

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1959 1. Golomb, M.; Weinberger, H.F.

Optimal approximation and error bounds.

On numerical approximation (Proc. Symp. Math. :Res. Center, Univ. Wisconsin, April 1958. Ed. by R.E. Langer), pp. 117-190. Univ. of Wisconsin Press, Madison, 1959. (MR ~' 12697; Zb

2!,

p. 58.)

1960

I. Birkhoff, G.; Garabedian, H.L. Smooth surface interpolation.

J. Math. and Phys. 39 (1960), 258-268. (MR 22, 10151; Zb ~' p. 129.) 2. Johnson, R.S.

On monosplines of least deviation.

Trans. Amer. Math. Soc. 96 (1960), 458-477. (~ 23, A270.) 3. Rutishauser, H.

Bemerkungen zur glatten Interpolation.

Z. Angew. Math. Phys.

l!

(1960), 508-513. (MR ~' 883.) 4. Schwerdtfeger, H.

Notes on numerical analysis. II: Interpolation and curve fitting by sectionally linear functions.

Canad. Math. Bull.

l

(1960), 41-57. (Zb 96, p. 103.) 1961

I. Schwerdtfeger, H.

Notes on numerical analysis. III: Further remarks on sectionally linear functions.

Canad. Math. Bull.

i

(1961), 53-55. (Zb 106, p. 109.) 2. Theilheimer, F.; Starkweather, W.

The fairing of ship lines on a high-speed computer.

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7

-3. Weinberger, H.F.

Optimal approximation for functions prescribed at equally spaced points.

1961/62

J. Res. Nat. Bur. Standards Sect. B 65 (1961), 99-104. (MR 25, 3616; Zb 168, p. 149.)

1962

I. Asker, B.

The spline curve, a smooth interpolating function used in numerical design of ship-lines.

BIT~ (1962), 76-82. (Zb ~' p. 81.)

2. Boor, C. de

Bicubic spline interpolation.

J. Math. and Phys. ~ (1962), 2I2-218. (MR 28, 1735; Zb 108, p. 271.)

3. Landis, F.; Nilson, E.N.

The determination of thermodynamic properties by direct differentia-tion techniques.

Progress in international research on thermodynamic and transport prop-erties (Second Symp. on Thermophysical Propprop-erties. Ed. by J.F. Masi and D.H. Tsai), pp. 218-227. Acad. Press, New York, 1962.

4. Petersen, I.

On a piecewise polynomial approximation (Russian; Estonian and German summaries).

Eesti NSV Tead. Akad. Toimetised Fuus.-Mat. II (1962), 24-32. (MR 25, 3307.)

5. Walsh, J.L.; Ahlberg, J.H.; Nilson, E.N.

Best approximation properties of the spline fit.

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I963

I. Ahlberg, J.H.; Nilson, E.N.

Convergence properties of the spline fit.

J. Soc. Indust. Appl. Math.

l l

(I963), 95-I04. (MR 27, 2763; Zb 196, p. 487.)

2. Boor, C. de

Best approximation properties of spline functions of odd degree, J. Math. Mech. 12 (1963), 747-749. (MR 27, 3982; Zb ~' p. 276.)

3. Sard, A.

Linear approximation.

American Mathematical Society, Providence, R.I., 1963. (MR 28, 1429; Zb

J..!1,

p • 54 • )

4.

Schaefer, H.

Latteninterpolation bei einer Funktion von zwei Veranderlichen. Z. Angew. Math. Phys.

Ji

(1963), 90-96. (Zb 108, p. 300.)

1964

I. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.

Fundamental properties of generalized splines.

Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1412-I419. (MR 36, 6846; Zb ]~, p. 362.)

2. Birkhoff, G.; Boor, C. de

Error bounds for spline interpolation.

J. Math. Mech.

ll

(1964), 827-835. (MR ~' 2583; Zb 144, p. 285.) 3. Collatz, L.

Einschliessungssatz fur die Minimalabweichung bei der Segmentapproxima-tion.

Simposio internazionale sulle applicazioni dell' Analisi alla Fisica Matematica (Cagliari-Sassari, 1964), pp. I1-21. Cremonese, Rome, 1965.

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9

-4. Ferguson, J.

Multivariable curve interpolation.

J. Assoc. Comput. Mach.

l l

(1964), 221-228. (MR 28, 5551; Zb 123, p. 330; CA ~, 1806.)

5. Greville, T.N.E.

Numerical procedures for interpolation by spline functions.

1964

SIAM J. Numer. Anal.

l

(1964), 53-68. (MR 36, 4784; Zb

l!L,

p. 336.) 6. Mehlum, E.

A curve-fitting method based on a variational criterion.

BIT~ (1964), 213-223. (MR 30, 4376.) 7. Schoenberg, I.J.

Spline interpolation and best quadrature formulae.

Bull. Amer. Math. Soc. 70 {1964), 143-148. (MR 28, 394; Zb 136, p. 362.) 8. Schoenberg, I.J.

Spline interpolation and the higher derivatives.

Proc. Nat. Acad. Sci. U.S.A.~ {1964), 24-28. (MR ~' 3278; Zb 136, p. 362.)

9. Schoenberg, I.J.

On best approximations of linear operators.

Nederl. Akad. Wetensch. Proc. Ser. A 67 {1964), 155-163. (MR 28, 4284; Zb 146, p. 85.)

10. Schoenberg, I.J.

On trigonometric spline interpolation.

J. Math. Mech.

l1

(1964), 795-825. (MR ~' 2589; Zb 147, p. 321.)

II. Schoenberg, I.J.

Spline functions and the problem of graduation.

Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 947-950. {MR 29, 5040; Zb 147, p. 321.)

On interpolation by spline functions and its minimal properties. On approximation theory {Proc. Con£. Oberwolfach, Aug. 1963. Ed. by P.L. Butzer and J. Korevaar), pp. 109-129. Birkhauser Verlag, Basel,

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1965

1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.

Best approximation and convergence properties of higher-order spline approximations.

J. Math. Mech. 14 (1965), 231-243. (MR 35, 5823; Zb ~' p. 68.) 2. Ahlberg, J.H., Nilson, E.N.; Walsh, J.L.

Convergence properties of generalized splines.

Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 344-350.

(MR

36, 6847; Zb 136, p. 363.)

3. Ahlberg, J.H.; Nilson, E.N.

Orthogonality properties of spline functions.

J. Math. Anal. Appl.

l!

(1965), 321-337. (MR 37, 660; Zb 136, p. 48.) 4. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.

Extremal, orthogonality, and convergence properties of multidimensional splines.

J. Math. Anal. Appl.

l!

(1965), 27-48. (MR

li•

661; Zb 136, P• 48.) 5. Atteia, M.

GenEhalisation de la definition et des proprietes des "spline fonctions". C.R. Acad. Sci. Paris Ser. A 260 (1965), 3550-3553. (MR

12.t

3340;

Zb 163, p. 377.)

6. Atteia, M.

nspline-fonctions" generalisees.

C. R. Acad. Sci. Paris Ser. A 261 (1965), 2149-2152. (MR 35, 3341.) 7. Birkhoff, G.; Boor, C.R. de

Piecewise polynomial interpolation and approximation.

Approximation of functions (Proc. Symp. on appr. functions, Gen. Motors Res. Lab., Warren, Michigan, 1964. Ed. by H.L. Garabedian), pp. 164-190. Elsevier, Amsterdam, 1965. (MR 32, 6646; Zb 136, p. 47.)

8. Schoenberg, I.J.

On monosplines of least deviation and best quadrature formulae.

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- 11 - 1965/66

9. Secrest, D.

Numerical integration of arbitrarily spaced data and estimation of errors.

SIAM J. Numer. Anal. £·(1965), 52-68. (MR

1!•

:4176; Zb 135, p. 386.) 10. Secrest, D.

Best approximate integration formulas and best error bounds.

Math. Comp.

I!

(1965), 79-83. (MR 33, 1967; Zb 134, p. 136; CA ~' 831.) 11. Secrest, D.

Error bounds for interpolation and differentiation by the use of spline functions.

SIAM J. Numer. Anal. ~·(1965), 440-447. (MR 33, 6231; Zb 144, p. 388.) 12. Wendroff, B.

Bounds for eigenvalues of some differential operators by the Rayleigh-Ritz method.

Math. Comp. 19 (1965), 218-224. (MR

ll•

4169.)

1966 1. Ahlberg, J.H.; Nilson, E.N.

The approximation of linear functionals.

l

(1966), 173-182. (MR 36, 589; Zb 147, p. 51.) 2. Atteia, M.

*

Etude de certains noyaux et theorie des fonctions "spline" en Analyse Numerique.

Universite de Grenoble. These. Grenoble, 1966.

3. Atteia, M.

Existence et determination des fonctions "spline"

a

plusieurs variables. C.R. Acad. Sci. Paris Ser. A 262 (1966), 575...:·578. (MR 33, 3004;

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4. Aubin, J.P.

*

Approximation des espaces de distributions et des operateurs differen-tiels.

These Doct. Sci. Math. Paris, 1966. (BS ~' 16561.) 5. Barrodale, I.; Young, A.

A note on numerical procedures for approximation by spline functions. Comput. J • .2_ (1966), 318-320. (MR 34, 2151; Zb 168, p. 149; CA.!.!_, 69.) 6. Birkhoff, G.; Boor,

c.

de; Swartz, B.; Wendroff, B.

Rayleigh-Ritz approximation by piecewise cubic polynomials.

l

(1966), 188-203. (MR 34, 3773; Zb 144, p. 380; CA ..!.Q., 3202.)

y

7. Birman, M.S.; Solomjak, M.Z.

Approximation of the functions of the classes ~ by piecewise

polynomi-p

al functions.

Dokl. Akad. Nauk SSSR

lZ!

(1966), 1015-1018 (Russian); translated as Soviet Math. Dokl.

L

(1966), 1573-1577. (MR 35, 630.)

8. Boor, C. de

*

The method of projections as applied to the numerical solution of two point boundary value problems using cubic splines (doctoral disserta-tion).

University of Michigan, Ann Arbor, 1966. (BS 29, I 0097; DA '!:]_, 3592-B.)

9. Boor, C. de; Lynch, R.E.

On splines and their minimum properties.

J. Math. Mech.

11

(1966), 953-969. (MR 34, 3159; Zb 185, p. 205.)

I 0. Caras so, C.

*

Methodes numeriques pour !'obtention de fonctions-spline. Universite de Grenoble. These. Grenoble, 1966. (BS 28, 6538.)

II. Ciarlet, P.G.

*

Variational methods for nonlinear boundary value problems (doctoral dissertation).

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12. Curry, H.B.; Schoenberg, I.J.

On folya frequency functions. IV: The fundamental spline functions and their limits.

J. Analyse Math.

ll

(1966), 71-107. (MR ~' 1884; Zb 146, p. 84.) 13. Ehlich, H.

Untersuchungen zur numerischen Fourieranalyse. Math. Z.

2l

(1966), 380-420. (MR 34, 7057.) 14. Glass, J.M.

Smooth-curve interpolation: a generalized spline-fit procedure.

BIT~ (1966), 277-293. (Zb 173, p. 186; CR ~' 12801.) 15. Handscomb, D.C.

Spline functions.

Methods of numerical approximation. Ed. by D.C. Handscomb, pp. 163-167. Pergamon Press, Oxfordt 1966.

16. Handscomb, D.C.

Optimal approximation by means of spline functions.

Methods of numerical approximation. Ed. by D.C. Handscomb, pp. 177-181. Pergamon Press, Oxford, 1966.

17. Innanen, K.A.

An example of precise interpolation with a spline function.

J. Computational Phys. (1966), 303-304. (CR ~' 12789; CA ~' 71.) 18. Karlin, S.; Studden, W.J.

Tchebycheff systems: with applications in analysis and statistics.

pp. 140-143; pp. 436-454.

Interscience, New York, 1966. (MR 34, 4757; Zb 153, p. 389.) 19. Karlin, S.; Ziegler, Z.

Chebyshevian spline functions.

l

(1966), 514-543. (MR 35, 7041; Zb

!I!'

p. 310.) 20. Malozemov, V.N.

On the deviation of broken lines (Russian, English summary). Vestnik Leningrad. Univ. ~no. 7 (1966), 150-153. (MR 33, 4533; Zb 177, p. 87.)

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21. Marsden, M.; Schoenberg, I.J.

On variation diminishing spline approximation methods. Mathematica (Cluj)!!' no, 31 (1966), 61-82. (MR 35, 4648; Zb .!.2.!_, p • 3 I 0 • )

22. Milnes, H.W.

A variational approach to smoothing unequally spaced data subject to random errors.

Indust. Math. 16 (1966), 77-93. (MR 40, 5108.) 23. Schoenberg, I.J.

On Hermite-Birkhoff interpolation.

J. Math. Anal. Appl. ~ (1966), 538-543. (MR 34, 3160; Zb 156, p. 287.) 24. Schoenberg, I.J.

On monosplines of least square deviation and best quadrature formulae. II.

l

(1966), 321-328. (MR 34, 3170; Zb 147, p. 321.) 25. Schumaker, L.L.

*

On some approximation problems involving Tchebycheff systems and spline functions (doctoral dissertation).

Stanford University, Stanford, 1966. (BS 29, 2535; DA

!L'

240-B.) 26. Schweikert, D.G.

*

The spline in tension (hyperbolic spline) and the reduction of extrane-ous inflection points (doctoral dissertation).

Brown University, Providence, 1966. (DA 28, 267-B.) 27. Schweikert, D.G.

An interpolation curve using a spline in tension.

J. Math. and Phys. 45 (1966), 312-317. (MR 34, 6990; Zb 146, p. 141.) 28. Sharma, A.; Meir, A.

Degree of approximation of spline interpolation.

J. Math. Mech. ~ (1966), 759-767. (MR ~' 3006; Zb 158, p. 307.) 29. Stern, M.D.

*

Some problems in the optimal approximation of bounded linear function-als (doctoral dissertation).

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- IS - 1966/67

30. Varga, R. S.

Hermite interpolation-type Ritz methods for two-point boundary value problems.

Numerical solution of partial differential equations (Proc. Symp. Univ. Maryland, 1965. Ed. by J.H. Bramble), pp. 365-373. Acad. Press, New York, 1966. (MR 34, 5302; Zb 1!!_, p. 357.)

1967 1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.

Complex cubic splines.

Trans. Amer. Math. Soc. 129 (1967), 391-413. (MR 36, 573; BS 29, 11591.) 2. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.

*

The theory of splines and their applications.

Acad. Press, New York, 1967. (MR 39, 684; Zb 158, p. 159.) 3. Atteia, M.

Sur les fonctions-spline generalisees.

Actes du 5e Congres de l'AFIRO, Lille, 1966, PP• 113-116. Assoc. Frany• d'Inform. et de Rech. Operat., Paris, 1967. 4. Atteia, M.

Fonctions "spline" avec contraintes lineaires de type inegalite. Actes du 6e Congres de l'AFIRO, Nancy, 1967, pp. 42-54.

Assoc. Frany• d'Inform. et de Rech. Operat., Paris, 1967. 5. Aubin, J.P.

Approximation des espaces de distributions et des operateurs differen-tiels.

Bull. Soc. Math. France, supplement au numero de Decembre 1967. Memoire no. 12. (BS 29, 9570.)

6. Aubin, J.P.

Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Galerkin's and finite differ-ence methods.

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7. Birkhof£, G.

Local spline approximation by moments.

J. Math. Mech.

li

(1967), 987-990. (MR 34, 8051; Zb 148, p. 292.) 8. Birkhoff, G.; Priver, A.

Hermite interpolation errors for derivatives.

J. Math. and Phys. 46 (1967), 440-447. (MR 36, 1883; Zb 176, p. 142.) 9. Carasso, C.

Obtention d'une fonction-Spline d'interpolation d'ordre K par une methode d'integration locale.

Procedures algol en analyse numerique, pp. 288-291.

Centre National de la Recherche Scientifique, Paris, 1967. 10. Carasso, C.

Methode pour l'obtention de fonctions-spline d'interpolation d'ordre deux.

Obtention d'une fonction lisse passant par des points donnes et ayant en ces points des derivees donnees (fonction-spline d'Hermite).

Centre National de la Recherche Scientifique, Paris, 1967. 12. Carasso, G.

Obtention de la derivee d'une fonction donnee par points. Procedures algol en analyse numerique, pp. 30Q-301.

Construction numer~que de fonctions-spline.

Actes du 5e Congres de l'AFIRO, Lille, 1966, pp. 506-509. Assoc. Fran)· d'Inform. et de Rech. Operat., Paris, 1967. 14. Carasso, C.

Methode generale de construction de fonctions spline.

Rev. Franyaise Informat. Recherche Operationelle

l•

no. 5 (1967), 119-127. (MR lZ_, 667; Zb 163, p. 377; BS 29, 13887.)

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- 17 - 1967

15. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.

Numerical methods of high-order accuracy for nonlinear boundary value problems. I: One dimensional problem.

Numer. Math. ~ (1967), 394-430. (MR 36, 4813; Zb 155, p. 204.) 16. Cybertowicz, Z.

On some approximation problems.

Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.

11

(1967), 497-501. (Zb 176, p. 352.)

17. Ferrand, C,

Lissage par utilisation de fonctions analogues aux fonctions spline. Actes du 6e Congres de l'AFIRO, Nancy, 1967, pp. 14-31.

Assoc. Franc. d'Inform. et de Rech. Operat., Paris, 1967. 18. Joly, J.L.

Spline functions, interpolation and numerical quadrature.

Mathematical methods for digital computers, Vol. II. Ed. by A. Ralston and H.S. Wilf, pp. 156-168. Wiley, New York, 1967. (CR ~' 12020.) 19. Joly, J.L.

Utilisation des fonctions spline pour le lissage.

Actes du 5e Congres de l'AFIRO, Lille, 1966, pp. 349-352. Assoc. Franc. d'Inform. et de Rech. Operat., Paris, 1967. 20. Joly, J.L.

Theoremes de convergence des fonctions spline generales d'interpola-tion et d'ajustement.

C.R. Acad. Sci. Paris Ser. A 264 (1967), 126-128. (MR 35, 3342; Zb ]54, p. 149; BS 28, 9341.)

21. Karlin, S.; Schumaker, L.L.

The fundamental theorem of algebra for Tchebycheffian monosplines. J. Analyse Math. 20 (1967), 233-270. (MR 36, 582; Zb 187, p. 20; BS ~' 4264.)

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22. Karlin, S.; Ziegler, Z.

Chebyshevian spline functions.

Inequalities (Proc. Symp. Wright-Patterson Air Force Base, Ohio, 1965. Ed. by 0. Shisha), pp. 137-149. Acad. Press, New York, 1967.

(MR ~' 1854; Zb

ll!'

p. 310.) 23. Loscalzo, F.R.; Talbot, T.D.

Spline function approximations for solutions of ordinary differential equations.

Bull. Amer. Math. Soc.

2l

(1967), 438-442. (MR 35, 1218; Zb

JI!,

p. 363.)

24. Loscalzo, F.R.; Talbot, T.D.

Spline function approximations for solutions of ordinary differential equations.

SIAM J. Numer. Anal.~ (1967), 433-445. (MR 36, 4808; Zb

lZ!'

p. 363; CA ~' 90.)

25. Malozemov, V.N.

Polygonal interpolation.

Mat. Zametki

l

(1967), 537-540 (Russian); translated as Math. Notes (1967), 355-357. (MR 35, 5816.)

26. Meinguet, J.

Optimal approximation and error bounds in seminormed spaces.

Numer. Math. 10 (1967), 370-380. (MR

lr'

6012; CA ~' 878; BS 29, 4620.) 27. Munteanu, M.J.

Observations on optimal solutions of some nonlinear differential pro-blems with boundary values in the subspace of generalized spline func-tions (Roumanian).

Bul. Sti. Inst. Politehn. Cluj.

lQ

(1967), 47-56. 28. Nord, S.

Approximation properties of the spline fit.

(22)

- 19 - 1967

29. Perrin, F.M.

*

An application of monotone operators to differential and partial dif-ferential equations on infinite domains (doctoral dissertation). Case Institute of Technology, Cleveland, 1967.

30. Reinsch, C.H.

Smoothing by spline functions.

Numer. Math. 10 (1967), 177-183. (Zb

l£l,

p. 362; CR ~' 14528.) 31. Rice, J.R.

Characterization of Chebyshev approximations by splines.

SIAM J, Numer. Anal.

i

(1967), 557-565. (MR 36, 6851; Zb 187, p. 329.) 32. Sard, A. Optimal approximation. J. Functional Analysis 33. Schoenberg, I.J. On spline functions. (1967), 222-244. (MR 36, 3037; Zb 158, p. 136.)

Inequalities (Proc. Symp. Wright-Patterson Air Force Base, Ohio, 1965. Ed. by 0. Shisha), pp. 255-291. Acad. Press, New York, 1967.

(MR 36, 6848.) 34. Schultz, M.H.; Varga, R.S. 1-splines. Numer. Math. 10 (1967), 345-369. (MR 37, 665; Zb 183, p. 444;

_--

---CA 12, 872.) 35. Stern, M.D.

Optimal quadrature formulae.

Comput. J. ~ (1967), 396-403. (MR 35, 3885; CA

!l,

836.) 36. Subbotin, Yu.N.

Piecewise-polynomial (spline) interpolation.

Mat. Zametki 1 (1967), 63-70 (Russian); translated as Math. Notes (1967), 41-45. (MR 35, 4645; Zb 159, p. 84.)

37. Young, J.D.

Numerical applications of cubic spline functions.

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Cubic splines on the real line.

J. Approximation Theory

l

(1968), 5-10. (MR 37, 6650; Zb 179, p. 365.) 2. Amunrud, L.R.

*

Tchebycheff approximations by general spline functions (doctoral dis-sertation).

Montana State University, Montana, 1968. (DA 29, 4254-B.) 3. Anselone, P.M.; Laurent, P.J.

A general method for the construction of interpolating or smoothing spline-functions.

Numer. Math.~ (1968), 66-82. (MR 40, 3145; Zb 197, p. 135; CAll' 55.) 4. Atkinson, K.E.

On the order of convergence of natural cubic spline interpolation. SIAM J. Numer. Anal.~ (1968), 89-101. (MR

lit

1853; Zb 208, P• 408.) 5. Atteia, M.

Fonctions "spline" definies sur un ensemble convexe.

Numer. Math.~ (1968), 192-210. (MR

iL'

2265; Zb 186, p. 452; BS 30, 6605.)

6. Aubin, J.P.

Interpolation et approximation optimales et "spline functions". J. Math. Anal. Appl. 24 (1968), 1-24. (MR

lr'

6651.)

7. Aubin, J.P.

Best approximation of linear operators in Hilbert spaces.

SIAM J. Numer. Anal.~ (1968), 518-521. (MR 38, 6743; Zb 176, p. 131.) 8. Bickley, W.G.

Piecewise cubic interpolation and two-point boundary problems. Comput. J.

l l

(1968), 206-208. (MR )7, 6036; Zb 155, p. 480;

(24)

- 21 - 1968

9. Birkhoff, G.; Schultz, M.H.; Varga, R.S.

Piecewise Hermite interpolation in one and two variables with applica-tions to partial differential equaapplica-tions.

Numer. Math.

l!

(1968), 232-256. (MR

ll,

2404; Zb 159, p. 209; CA

g,

2291.)

10. Birkhoff, G.; Gordon, W.J.

The draftsman's and related equations.

l

(1968), 199-208. (MR 38, 4055.)

I 1 • Boor, C. de

On local spline approximation by moments.

J. Math. Mech.

ll

(1968), 729-735. (MR 36, 6850; Zb 162, p. 84.) 12. Boor, C. de

On the convergence of odd-degree spline interpolation.

l

(1968), 452-463. (MR 38, 6273; Zb 174, p. 99.) 13. Boor, C. de

On uniform approximation by splines.

l

(1968), 219-235. (MR 39, 1866; Zb 193, p. 25.) 14. Buchanan, J.E.; Thomas, D.H.

On least-squares fitting of two-dimensional data with a special struc-ture.

SIAM J. Numer. AnaL

1

(1968), 252-257. (MR

ll,

3740.) 15. Bulirsch, R.; Rutishauser, H.

Spline-Interpolation.

Mathematische Hilfsmittel des Ingenieurs, Vol. III. Ed. by R. Sauer ancl. I. Szabo, pp. 265-277. Springer, Berlin, 1968. (MR 37, 7115;

_-

--Zb 193, p. 352.) 16. Cheney, E. W. ; Schurer, F.

A note on the operators arising in spline approximation.

J. Approximation Theory (1968), 94-102. (MR 37, 5580; Zb 177, p. 89.) 17. Cherruault, Y.

*

Approximation d'operateurs lineaires et applications. These, Paris, 1966.

Monographies d'Informatique, Vol. 4. Dunod, Paris, 1968. (MR 38, 4879; Zb 169, p. I 96.)

(25)

18. Ciarlet, P.G.

An O(h2) method for a non-smooth boundary value problem.

Aequationes Math.

l

(1968), 39-49. (MR 38, 869; Zb 159, p. 117.) 19. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.

Numerical methods of high-order accuracy for nonlinear boundary value problems. II: Nonlinear boundary conditions.

Numer. Math, II (1968), 331-345. (MR

lL'

4965; Zb ~' p. 149; CA .!1_, 2548.)

Numerical methods of high-order accuracy for nonlinear boundary value problems. III: Eigenvalue problems.

Numer. Math. 12 (1968), 120-133. (MR 38, 1838; Zb ~' p. 183; CA .!1_, 2 77. )

Numerical methods of high-order accuracy for nonlinear boundary value problems. IV: Periodic boundary conditions.

Numer. Math.

g

(1968), 266-279. (MR 39, 2337; Zb ~, p. 183.) 22. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.

Numerical methods of high-order accuracy for nonlinear two-point bound-ary value problems.

Programmation en Mathematiques Numeriques (Coll. Intern.CNRS,no. 165,

Besa~so~ 1966), pp. 217-225. Centre National de la Recherche Scienti-fique, Paris, 1968. (MR 38s 1837; Zb 207, p. 164.)

23. Cybertowicz,

z.

On some approximation problems.

Frace Mat. 12 (1968), 61-74. (MR 38, 2496.) 24. Diringer, P.

Interpolation, derivation et integration

a

l'aide de fonctions spline. Recherche Aerospat. 124 (1968), 13-16. (BS 30, 5046.)

25. Einarsson, B.

Numerical calculation of Fourier integrals with cubic splines. BIT 8 (1968), 279-286. (MR 39, 1114; Zb 187, p. 105; CA 13, 542.)

(26)

23

-26. Eltom, M.E.A.

*

Numerical approximation of functions of one ore more variables (doctoral dissertation).

Oxford University, Oxford, 1968. 27. Fix, G.

1968

*

Bounds and approximations for eigenvalues of self-adjoint boundary value problems (doctoral dissertation).

Harvard University, Cambridge (Mass.), 1968. 28. Golomb, M.

Approximation by periodic spline interpolants on uniform meshes.

l

(1968), 26-65. (MR 38, 1444; Zb 185, p. 309.) 29. Hall, C.A.

On error bounds for spline interpolation.

l

(1968), 209-218. (MR 39, 681; Zb 177, p. 89.) 30. Herbold, R.J.

*

Consistent quadrature schemes for the numerical solution of boundary value problems by variational techniques (doctoral dissertation). Case Western Reserve University, Cleveland, 1968. (CR ~' 15006; DA 30, 165-B.)

31. Hulme, B.L.

Interpolation by Ritz approximation.

J. Math. Mech. ~ (1968), 337-341. (MR

lL•

7090; Zb 165, p. 386.) 32. Ikaunieks, E.A.; Ermu~a, A.E.

Concave piecewise-polynomial interpolation. (Russian; Latvian and English summaries.)

Latvian Math. Yearbook, Vol. 4, pp. 149-163. Izdat. "Zinatne", Riga, 1968. (MR 39, 2293; Zb 208, p. 409.)

33. Jerome, J.W.; Schumaker, L.L.

A note on obtaining natural spline functions by the abstract approach of Atteia and Laurent.

SIAM J. Numer. Anal. 5 (1968), 657-663. (MR 40, 6127; Zb 185, p. 409; BS 30 , 14 544 . )

(27)

34. Johnson, O.G.

*

Convergence, error bounds, sensitivity, and numerical comparisons of certain absolutely continuous Rayleigh-Ritz methods for Sturm-Liouville eigenvalue problems (doctoral dissertation).

University of California, Berkeley, 1968. (DA ~. 3396-B.)

35. Karlin, S.

Total positivity, Vol. I. pp. 357-364; pp. 501-564.

Stanford Univ. Press, Stanford, California, 1968. (MR 37, 5667.) 36. Karlin, S.; Karon, J.M.

A variation-diminishing generalized spline approximation method. J. Approximation Theory (1968), 255-268. (MR 38, 3664;

Zb 165, P• 386.) 37. Karon, J.M.

*

The sign-regularity properties of a class of Green's functions for ordinary differential equations and some related results (doctoral dissertation).

Stanford Univ., Stanford, California, 1968. (DA ~' 2529-B.) 38. Laurent, P.J.

Representation de donnees experimentales

a

l'aide de fonctions-spline d'ajustement et evaluation optimale de fonctionnelles lineaires conti-nues.

Apl. Mat.~ (1968), 154-162. (MR 38, 4000; Zb 155, p. 219.) 39. Laurent, P.J.

Theoremes de characterisation en approximation convexe. Mathema.tica (Cluj)

.!.Q.,

no. 33 (1968), 95-111 •. (MR ±.!_, 701.) 40. Loscalzo, F.R.

*

On the use of spline functions for the numerical solution of ordinary differential equations (doctoral dissertation).

Univ. of Wisconsin, Madison, 1968. (DA 29, 2983-B.) 41. Marsden, M.J.

*

An identity for spline functions with applications to variation-dimin-ishing spline approximation (doctoral dissertation).

(28)

25

-42. Meir, A.; Sharma, A.

One-sided spline approximation.

Studia Sci. Math. Hungar.

1

(1968), 211-218. (MR 38, 1445; Zb 175, p. 350.)

43. Meir, A.; Sharma, A.

Convergence of a class of interpolatory splines.

l

(1968), 243-250. (MR 38, 3665; Zb 186, p. I 14. )

44. Phillips, G.M.

Algorithms for piecewise straight line approximations.

Comput. J.

!l

(1968), 211-212.

OKR

~' 6013; Zb 165, p. 512; CA _!!, 2529.)

45. Powell, M.J.D.

On best L₂spline approximations.

1968

Numerische Mathematik, Differentialgleichungen, Approximationstheorie (Proc. Conf. Oberwolfach, 1966. Ed. by L. Collatz, G. Meinardus and H. Unger), pp. 317-339. Birkhauser Verlag, Basel, 1968.

46. Sard, A.

Optimal approximation: an addendum.

J. Functional Analysis~ (1968), 368-369. (MR 38, 1457; Zb 159, p. 438.) 47. Schoenberg, I.J.

On the Ahlberg-Nilson extension of spline interpolation: the g-splines and their optimal properties.

J. Math. Anal. Appl. 21 (1968), 207-231. (MR 36, 6849; Zb 159, p. 84.) 48. Schoenberg, I.J.

On spline interpolation at all integer points of the real axis. Mathematica (Cluj)

lQ,

no. 33 (1968), 151-170. (MR 3~, 6274; Zb 183, p. 331.)

Abhandlungen aus Zahlentheorie und Analysis. Ed. by P. Turan, pp. 279-295. Deutscher Verlag der Wissenschaften, Berlin, 1968. (Zb 198, p. 90.)

(29)

50. Schumaker, L.L.

Uniform approximation by Tchebycheffian spline functions.

J. Math. Mech. ~ (1968), 369-377. (MR 39, 3203, Zb ~' p. 386.) 51. Schumaker, L.L.

Uniform approximation by Chebyshev spline functions. II: Free knots. SIAM J. Numer. Anal. ~ (1968), 647-656. (MR 39, 3204; Zb 169, p. 394.) 52. Schurer, F.

A note on interpolating periodic quintic splines with equally spaced nodes.

J. Approximation Theory! (1968), 493-500. (MR 38, 6275; Zb 186, p. 114.)

53. Schurer, F.; Cheney, E.W.

On interpolating cubic splines with equally-spaced nodes.

Nederl. Akad. Wetensch. Proc. Ser. A

2!

(1968), 517-524. (MR 40, 6129; Zb 184, p. 379.)

54. Shisha,

o.

Trends in approximation theory.

Appl. Mech. Rev.~ (1968), 337-341. (BS 30, 2197.) 55. Simpson, R.B.

Approximation of the minimizing element for a class of functionals. SIAM J. Numer. Anal. 5 (1968), 26-41. (MR

lL'

3414; CA ~' 1956.) 56. Smirnov, V.M.

A certain method of smooth interpolation of functions.

Z. Vy~isl. Mat. i Mat. Fiz. ~ (1968), 1330-1331 (Russian); translated as U.S.S.R. Comput. Math. and Math. Phys. ~~ no. 6 (1968), 190-193.

(MR ~' 5839.)

57. Spath, H.

Ein Verfahren zur flachentreuen Approximation von Treppenfunktionen durch glatte Kurven.

Z. Angew. Math. Mech. 48 (1968), T106-T107. (BS 30, 18375.) 58. Studden, W.J.; Van Arman, D.J.

Admissible designs for polynomial spline regression. Ann. Math. Statist. 40 (1968), 1557-1569. (MR 40, 2195.)

(30)

27

-59. Swartz, B.

O(h2n+2-Q.) b oun s on some sp 1ne 1nterpo at1on errors. d 1' . 1 . Bull. Amer. Math. Soc. 74 (1968), 1072-1078. (MR 38, 4869; Zb

.!.!!_,

p. 340.)

60. Van Arman, D.J.

1968/69

*

Classification of experimental designs relative to polynomial spline regression functions (doctoral dissertation).

Purdue University, Lafayette, 1968. (DA 29, 3967-B.) 61. Young, J.D.

Numerical applications of hyperbolic spline functions.

The Logistics Review

i•

no. 19 (1968), 17-22. (CR

!!'

19817.) 62. Young, J.D.

Numerical applications of damped cubic spline functions. The Logistics Review

i'

no. 20 (1968), 33-37. (CR

!l'

19818.)

Properties of analytic splines. I: Complex polynomial splines.

J. Math. Anal. Appl. 27 (1969), 262-278. (Zb 185, p. 135; BS

1!,

3145.) 2. Ahlberg, J.H.

Splines in the complex plane.

Approximations with special emphasis on spline functions. Ed. by

I.J. Schoenberg, pp. i-27. Acad. Press, New York, 1969. (MR

il'

2264.) 3. Albasiny, E.L.; Hoskins, W.D.

Cubic spline solutions to two-point boundary value problems. Comput. J.

ll

(1969), 151-153. (MR 39, 3710; Zb 185, p. 414; CA _!1, 3112.)

4. Amos, D.E.; Slater, M.L.

Polynomial and spline approximation by quadratic programming. Comm. ACM ~ (1969), 379-381. (Zb 187, p. 127; CAll' 2422.)

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5. Barnhill, R.E.; Wixom, J.A.

An error analysis for the bivariate interpolation of analytic functions. SIAM J. Numer. Anal.~ (1969), 450-457. (Zb 187, p. 501.)

6. Bellman, R.; Roth, R.

Curve fitting by segmented straight lines.

J. Amer. Statist. Assoc. 64 (1969), 1079-1084. (MR 39, 7760.) 7. Bickley, W.G.

Piecewise cubic interpolation and two-point boundary problems. (Letter to the editor.)

Comput. J. 12 (1969), 105. (CA

!l'

2789.)

8. Birkhoff, G.

Numerical solution of elliptic equations.

Lecture series in differential equations, vol. II. Ed. by A.K. Aziz, pp. 197-232. Van Nostrand Reinhold Company, New York, 1969.

(Zb 208, p. 192.)

9. Birkhoff, G.

Piecewise bicubic interpolation and approximations in polygons. Approximation with special emphasis on spline functions. Ed. by I.J. Schoenberg, pp. 185-221. Acad. Press, New York, 1969. 10. Blue, J .L.

Spline function methods for nonlinear boundary-value problems. Comm. ACM

I! (1969), 327-330. (Zb 175, p.

161; CR

lQ,

17706; CA _!2, 2032.)

1 I . Boor, C. de

On the approximation by y-polynomials.

Approximations with special emphasis on spline functions. Ed. by I.J. Schoenberg, pp. 157-183. Acad. Press, New York, 1969.

(MR ~' 4096.)

12. Carasso, C.; Laurent, P.J.

On the numerical construction and the practical use of interpolating spline functions.

Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968. Ed. by A.J.H. Morrell), Vol. I - Mathematics, Software, pp. 86-89.

North-Holland Publishing Company, Amsterdam, 1969. (MR 40, 8219; Zbl2..!_, p. 449; CA~, 1477.)

(32)

- 29 - 1969

Numerical methods of high-order accuracy for nonlinear boundary value problems. V: Monotone operator theory.

Numer. Math.

ll

(1969), 51-77. (MR 40, 3730; Zb ~' p. 186; CAll, 2420.)

14. Dailey, J.W.

*

Approximation by spline-type functions and related problems (doctoral dissertation).

Case Western Reserve University, Cleveland, 1969. (DA

1!,

3537-B.) 15. Elhay, S.

Optimal quadrature.

Bull. Austral. Math. Soc.! (1969), 81-108. (MR

!!'

2925; Zb 175, p. 351.)

16. Esch, R.E.; Eastman, W.L.

Computational methods for best spline function approximation.

J. Approximation Theory! (1969), 85-96. (MR 39, 1867; Zb ~' p. 176.)

17. Fitzgerald, C.H.; Schumaker, L.L.

A differential equation approach to interpolation at extremal points. J. Analyse Math. 22 (1969), 117-134. (MR

!!'

2257; BS

1!,

15430.) 18. Fix, G.

Higher-order Rayleigh-Ritz approximations.

J. Math. Mech. ~ (1969), 645-657. (MR 39, 2349.) 19. Fix, G.; Strang, G.

Fourier analysis of the finite element method in Ritz- Galerkin theory. Studies in Appl. Math. 48 (1969), 265-273. (MR s..!_. 2944;

Zb 179, p. 225.) 20. Fyfe, D.J.

The use of cubic splines in the solution of two-point boundary value problems.

Comput. J.

l!

(1969), 188-192. Q{R 39, 5065; Zb 185, p. 414; CA

ll' 3137.)

(33)

21. Golomb, M.

Spline interpolation near discontinuities.

I.J. Schoenberg, pp. 51-74. Acad. Press, New York, 1969. (MR

il,

693.) 22. Gordon, W.J.

Distributive lattices and the approximation of multivariate functions. Approximations with special emphasis on spline functions. Ed. by

I.J. Schoenberg, pp. 223-277. Acad. Press, New York, 1969. 23. Gordon, W.J.

Spline-blended surface interpolation through curve networks. J. Math. Mech. 18 (1969), 931-952. (MR 39, 7333; Zb 192, p. 422; BS 30, 803.)

24. Greville, T.N.E.

*

Theory and applications of spline functions.

Proc. Seminar Math. Res. Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville.

Acad. Press, New York, 1969. (MR 38, 3663.) 25. Greville, T.N.E.

Introduction to spline functions.

Theory and applications of spline functions (Proc. Seminar Math. Res. Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 1-35. Acad. Press, New York, 1969. (MR 39, 1868.)

26. Hall, C.A.

Error bounds for periodic quintic splines.

Comm. ACM ~ (1969), 450-452. (Zb 185, p. 408; CR

!l'

18293; CA ~, 2778.)

27. Hall, C.A.

Bicubic interpolation over triangles.

(34)

- 31 - 1969

28. Heindl, G.

Spline-Funktionen meh~erer Verinderlicher. I: Definition und Erzeugung durch Integration.

Bayer. Akad. Wiss. Math.-Natur. Kl. S.-B. (1969), 49-63. (BS 32, 5690.) 29. Herbold, R.J.; Schultz, M.H.; Varga, R.S.

The effect of quadrature errors in the numerical solution of boundary value problems by variational techniques.

Aequationes Math.

l

(1969), 247-270. Of[

!!•

6410; Zb 196, p. 176.) 30. Hilbert, S.R.

*

Numerical methods for elliptic boundary problems (doctoral disserta-tion).

University of Maryland, College Park, 1969. (DA

lL•

1399-B.) 31. Hill, I.D.

Note on algorithm 40: Spline interpolation of degree three. Comput. J. ~ (1969), 409.

32. Hulme, B.L.

*

Piecewise bicubic methods for plate bending problems (doctoral disser-tation).

Harvard University, Cambridge (Mass.), 1969. 33. Jerome, J.W.; Varga, R.S.

Generalizations of spline functions and applications to nonlinear boundary value and eigenvalue problem..

Theory and applications of spline functions (Proc. Seminar Math. Res. Ceriter, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp.

103-155. Acad. Press, New York, 1969. (MR 39, b85; Zb 188, p. 130.) 34. Jerome, J.W.; Schumaker, L.L.

On Lg-splines.

J. Approximation Theory! (1969), 29-49. (MR 39, 3201; Zb 172, p. 345.) 35. Jerome, J.W.; Schumaker, L.L.

Characterizations of functions with higher order derivatives in L •

p

(35)

36. Johnson, O.G.

Error bounds for Sturm-Liouville eigenvalue approximations by several piecewise cubic Rayleigh-Ritz methods.

SIAM J. Numer. Anal. 6 (1969), 317-333. (MR

!l•

4789; Zb 183, p. 446.) 37. Karlin, S.

Best quadrature formulas and interpolation by splines satisfying bound-ary conditions.

(MR

!it

2275.) 38. Karlin, S.

The fundamental theorem of algebra for monosplines satisfying certain boundary conditions and applications to optimal quadrature formulas. Approximations with special emphasis on spline functions. Ed. by I.J. Schoenberg, pp. 467-484. Acad. Press, New York, 1969.

(MR

!it

2276.) 39. Karon, J .M.

The sign-regularity properties of a class of Green's functions for ordinary differential equations.

J. Differential Equations~ (1969), 484-502. (MR

iL•

3863.)

~~ y

r

39a. Korne1cuk, N.P.; Luspa1, N.E.

Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation.

Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 1416-1437 (Russian); trans-lated as Math. USSR·-Izv.

l

(1 969), 1335-J 355. (Zb 198, p. 89.)

40. Krinzesza, F.

*

Zur periodischen Spline-Interpolation (doctoral dissertation). Ruhr-Universitat, Bochum, 1969.

41. Lathrop, J.F.

*

Application of spline functions to the numerical solution of ordinary and partial differential equations (doctoral dissertation).

University of Colorado, Boulder, 1969. (DA 30, 4701-B.) 42. Laurent, P.J.

Construction of spline functions in a convex set.

(36)

- 33 - 1969

43. Lee, J.W.

*

The study of a class of boundary value problems with cyclic totally positive Green's functions with applications to spline approximation and eigenvalue problems (doctoral dissertation).

Stanford University, Stanford, California, 1969. (DA

1Q,

1244-B.) 44. Loginov, A.S.

Approximation of continuous functions by broken lines.

Mat. Zametki ~ (1969), 149-160 (Russian); translated as Math. Notes 6 (1969), 549-555. (MR ~' 687; Zb 177, p. 88.)

45. Loscalzo, F.R.

An introduction to the application of spline functions to initial value problems.

Theory and applications of spline functions (Proc. Seminar Math. Res. Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 37-64. Acad. Press, New York, 1969. (MR 39, 2334; Zb

12!'

p. 165.)

46. Mangasarian, O.L.; Schumaker, L.L. Splines via optimal control.

(MR ~, 4073.) 47. Mansfield, L.E.

*

Optimal approximation and error bounds 1n spaces of multivariate func-tions (doctoral dissertation).

University of Utah, Salt Lake City, 1969. (DA 30, 2298-B.) 48. Meir, A.; Sharma, A.

On uniform approximation by cubic splines.

J. Approximation Theory! (1969), 270-274. (MR 40, 3137; Zb 183, p. 330.)

49. Morin, M.

*

Methodes de calcul des fonctions "spline" dans un ·convexe. Universite de Grenoble. These. Grenoble, 1969. (BS

ll'

17640.)

(37)

50. Murty, V.N.

*

Optimal designs of individual regression coefficients with a

Tchebycbeffian spline regression function (doctoral dissertation). Purdue University, Lafayette, 1969. (DA 30, 5283-B.)

51. Natterer, F.

Numerische Behandlung singularer Sturm-Liouville-Probleme. Numer. Math.

11

(1969), 434-447. (MR 40, 5143; Zb 182, p. 497.) 52. Nitsche, J.

Satze vom Jackson-Bernstein-Typ fur die Approximation mit Spline-Funktionen.

Math.

z.

109 (1969), 97-106. (MR 39, 4567; Zb 174, p. 355.) 53. Nitsche, J.

Orthogonalreihenentwicklung nach linearen Spline-Funktionen.

J. Approximation Theory! (1969), 66-78. (MR 40, 4653; Zb 174, p. 360.) 54. Nitsche, J.

Umkehrsatze fur Spline-Approximationen.

CompositioMath.~ (1969), 400-416. (MR ~, 4074; Zb 199, p. 393.) 55. Nitsche, J.

Eine Bemerkung zur kubischen Spline-Interpolation.

Abstract spaces and approximation (Proc. Con£. Oberwolfach, 1968. Ed. by P.L. Butzer and B.S. Nagy), pp. 367-372. Birkhauser Verlag, Basel, 1969. (MR ~~ 7344; Zb 202, P• 158; BS

11,

9425.)

56. Nitsche, J.

Verfahren von Ritz und Spline-Interpolation bei Sturm-Liouville-Randwertproblemen.

Numer. Math.

ll

(1969), 260-265. (Zb j!!, p. 182; CR

!l'

18291.) 57. Perrin, F.M.; Price, H.S.; Varga, R.S.

On higher-order numerical methods for nonlinear two-point boundary value problems.

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- 35 - ₁₉₆₉

58. Pierce, J.G.

*

Higher order convergence results for the Rayleigh-Ritz method applied to a special class of eigenvalue problems (doctoral dissertation). Case Western Reserve University, Cleveland, 1969.(DA 30, 4264-B.) 59. Powell, M.J.D.

A comparison of spline approximations with classical interpolation methods.

Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968. Ed. by A.J.H. Morrell), Vol. I -Mathematics, Software, pp. 95-98.

North-Holland Publishing Company, Amsterdam, 1969. (MR 40, 8223; Zb 194, p. 4 71; CA ~' 146 7.)

60. Powell, M.J.D.

The local dependence of least squares cubic splines.

SIAM J. Numer. Anal.~ (1969), 398-413. (MR

il'

1192; Zb 183, p. 441.) 61 • Rice, J. R.

The approximation of functions. Vol. II: Nonlinear and multivariate theory. pp. 123-167.

Addison-Wesley, Reading, 1969. (MR 39, 5989; Zb 185, p. 306.) 62. Rice, J.R.

On the degree of convergence of nonlinear spline approximation. Approximations with special emphasis on spline functions. Ed. by I.J. Schoenberg, pp. 349-365. Acad. Press, New York, 1969.

(MR 42, 2226.) 63. Ritter, K.

Generalized spline interpolation and nonlinear programming. Approximations with special emphasis on spline functions. Ed. by I.J. Schoenberg, pp. 75-117. Acad. Press, New York, 1969.

64. Ritter, K.

Two dimensional splines and their extremal properties.

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65. Rivlin, T.J.

An introduction to the approximation of functions. pp. 104-119. Blaisdell P.C., Waltham, 1969. (MR 40, 3126; Zb 189, p. 66.) 66. Sakai, M.

Error estimation on piecewise Hermite interpolation.

Mem. Fac. Sci. Kyushu Univ. Ser. A 23 (1969), 71-78. (Zb 201, p. 77.) 67. Schaback, R.

*

Spezielle rationale Splinefunktionen (doctoral dissertation). Universitat Munster, 1969.

Monosplines and quadrature formulae.

Theory and applications of spline functions (Proc. Seminar Math. Res. Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 157-207. Acad. Press, New York, 1969. (MR 39, 3202; Zb 203, p. 370.) 69. Schoenberg, I.J.

*

Approximations with special emphasis on spline functions.

Proc. Symp. Math. Res. Center, Univ. Wisconsin, May 1969. Ed. by

I. J. Schoenberg.

Acad. Press, NewYork,·1969. (MR40, 4638.) 70. Schoenberg, I.J.

Cardinal interpolation and spline functions.

J. Approximation Theory~ (1969), 167-206. (MR ~~ 2266; Zb 202, p. 348.)

Number theory and analysis (papers in honor of Edmund Landau), pp. 279-295. Plenum, New York, 1969. (MR

il'

5848.)

72. Schultz, M.H.

Multivariate spline functions and elliptic problems.

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37

-73. Schultz, M.H.

Multivariate L-spline interpolation.

J. Approximation Theory~ (1969), 127-135. (MR 40, 3138; Zb 202, p. 349.)

74. Schultz, M.H.

100-multivariate approximation theory.

1969

SIAM J. Numer. Anal. ~ (1969), 161-183. (MR 40, 4639a; Zb 202, p. 159; CA ~' 76.)

75. Schultz, M.H.

12-multivariate approximation theory.

SIAM J. Numer. Anal. ~ (1969), 184-209. (MR 40, 4639b; Zb 202, p. 159; CA ~' 77.)

76. Schultz, M.H.

L2-approximation theory of even order multivariate splines.

SIAM J. Numer. Anal..£_ (1969), 467-475. (MR i!._, 1193; Zb 198, p. 400.) 77. Schultz, M.H.

Rayleigh-Ritz-Galerkin methods for multidimensional problems.

SIAM J. Numer. Anal • .£_ (1969), 523-538. (MR i!._, 7859; Zb ~' p. 193; CR

1!,

20346; CA ~' 1193.)

78. Schultz, M.H.

Approximation theory of multivariate spline functions in Sobolev spaces.

SIAM J. Numer. Anal • .£_ (1969), 570-582. (MR i~' 7823; Zb ~' p. 188; CA ~' I 179.)

79. Schultz, M.H.

The Galerkin method for nonselfadjoint differential equations.

J. Math. Anal. Appl. 28 (1969), 647-651. (Zb 197, p. 137.) 80. Schumaker, 1.1.

Approximation by splines.

Theory and applications of spline functions (Proc. Seminar Math. Res. Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 65-85. Acad. Press, New York, 1969. (MR 39, 686; Zb 187, p. 328.)

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81. Schumaker, L.L.

Some algorithms for the computation of interpolating and approximating spline functions.

Theory and applications of spline functions (Proc. Seminar Math. Res. Center, Univ. Wisconsin, Oct. 1968. Ed. by T.N.E. Greville), pp. 87-102. Acad. Press, New York, 1969. (MR 39, 687; Zb 188, p. 223.)

82. Schumaker, L.L.

On the smoothness of best spline approximations.

J. Approximation Theory~ (1969), 410-418. (MR

il'

4076; Zb 183, p. 59.) 83. Sharma, A.; Meir, A.

Convergence of a class of interpolatory splines.

Abstract spaces and approximation (Proc. Conf. Oberwolfach, 1968. Ed. by P.L. Butzer and B.S. Nagy), pp. 373-374·. Birkhauser Verlag, Basel, 1969. (Zb 187, p. 329.)

84. Sims, S.E.

*

Convergence properties of spline functions (doctoral dissertation). University of Arizona, Tucson, 1969. (DA 30, 3763-B.)

85. Sonneveld, P.

Errors in cubic spline interpolation.

J. Engrg. Math. 1_ (1969), 107-117. (MR 40, 601; Zb 183, P• 442.)

86. Spath, H.

Algorithmus 10: Zweidimensionale glatte Interpolation; Twodimensional smooth interpolation.

Computing (Arch. Elektron. Rechnen) 4 (1969), 178-182. (CA

!l'

2431; BS l.!_, 3141 • )

87. Spath, H.

Exponential spline interpolation.

Computing (Arch. Elektron. Rechnen) ~ (1969), 225-233. (MR 40, 2216; Zb 184, p. 198; CR

l!'

18512; CA

11,

3156; BS 30, 8074.)

88. Spath, H.

Algorithm 40: Spline interpolation of degree three. Comput. J. 12 (1969), 198-199. (CA

!l'

3144b.)

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- 39 -

/

f

89. Spath, H.

Algorithm 42: Interpolation by certain quintic splines. Comput. J. 12 (1969), 292-293. (CA ~' 356b.)

90. Spath, H.

1969

*

Die numerische Berechnung von interpolierenden Spline-Funktionen mit Blockunterrelaxation (doctoral dissertation).'

Universitat Karlsruhe, 1969. 91. Stephens, A.B.

*

Convergence of the residual for Ritz-Galerkin approximation (doctoral dissertation).

University of Maryland, College Park, 1969. (DA

ll'

296-B.) 92. Storchai, V.F.

The deviation of polygonal functions in the L metric. _p

Mat. Zametki 5 (1969), 31-37 (Russian); translated as Math. Notes 5 (1969), 21-25. (MR 39, 688; Zb 177, p. 88.)

93. Swartz, B.; Wendroff, B.

Generalized finite-difference schemes.

Math. Comp. 23 (1969), 37-49. (MR 39, 1125; Zb 184, p. 385.) 94. Tihomirov, V.M.

Best methods of approximation and interpolation of differentiable func-tions in the space C[-1,1].

Mat. Sb. 80, no. 122 (1969), 290-304 (Russian); translated as Math. USSR-·Sb. 2_ (1969), 275-289. (MR 41, 703; Zb 204, p. 133.)

95. Varga, R.S.

Error bounds for spline interpolation.

I.J. Schoenberg, pp. 367-388. Acad. Press, New York, 1969. (MR 40, 6130.)

96. Wakoff, G.I.

*

Piecewise polynomial spaces and their use with the Rayleigh-Ritz-Galerkin method (doctoral dissertation).

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97. Wendroff, B.

First principles of numerical analysis. pp. 62-67.

Addison-Wesley, Reading, 1969. (Zb 194, p. 178; BS 30, 18456.) 98. Woodford, C.H.

Smooth curve interpolation.

BIT~ (1969), 69-77. (CR

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18077.) 99. Young, J.D.

Generalization of segmented spline fitting of third order. The Logistics Review

1,

no. 23 (1969), 33-40. (CR

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19819.) 100. Ziegler,

z.

One-sided L

1-approximation by splines of an arbitrary degree. Approximations with special emphasis on spline functions. Ed. by I.J. Schoenberg, pp. 405-413. Acad. Press, New York, 1969.

(MR40, 7684.)

1970

I. Ahlberg, J.H.

Spline approximation and computer-aided design.

Advances in Computers, Vol. 10. Ed. by F.L. Alt and M. Rubino££, pp. 275-289. Acad. Press, New York, 1970. (BS 32, 5046.)

2. Ahlberg, J.H; Nilson, E.N.

Polynomial splines on the real line.

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(1970), 398-409.

2a. Akima, H.

A new method of interpolation and smooth curve fitting based on local procedures.

J. Assoc. Comput. Mach. 17 (1970), 589-602. (Zb 209, p. 468.)

3. Atteia, M.

Fonctions "Spline" et noyaux reproduisants d'Aronszajn-Bergman. Rev. Fran~aise Informat. Recherche Operationnelle ~ (1970), 31-43.

(BS 32, 4653.) 4. Barrar, R.B.; Loeb, H.L.

Existence of best spline approximations with free knots.

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- 41 - 1970

5. Birkhoff, G.; Fix, G.

Accurate eigenvalue computations for elliptic problems.

Numerical solution of field problems in continuum physics (SIAM-AMS Proc.), vol. II, pp.Ill-151. Amer. Math. Soc., Providence, R.I., 1970.

(MR i!_, 4827.)

6. Bramble, J.H.; Hilbert, S.R.

Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation.

l

(1970), 112-124. (MR i!_, 7819; Zb 201, p. 78; CR ~' 19963; CAli' 2086.)

7. Bramble, J.H.; Schatz, A.H.

Rayleigh-Ritz-Galerkin methods for Dirichlet's problem using subspaces without boundary conditions.

Comm. Pure Appl. Math. 23 (1970), 653-675. (MR 42, 2690; Zb 195, p. 388.)

8. Cavaretta, A.S. jr.

*

On cardinal perfect splines of least sup norm on the real axis (doctoral dissertation).

University of Wisconsin, Madison, 1970. (DA

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674G-B.) 9. Chan, P.P.-Y.

*

Approximation theory with emphasis on spline functions and applications to differential and integral equations (doctoral dissertation).

Case Western Reserve University, Cleveland, 1970. (DA l!_, 4191-B.) 10. Cheney, E.W.; Schurer, F.

Convergence of cubic spline interpolants.

2

(1970), 114-116. (MR 40, 7680; Zb 193, p. 25; BS 30, 12879.)

II. Cheney, E.W.; Price, K.H. Minimal projections.

Approximation theory (Proc. Symp., Lancaster, July 1969. Ed. by A. Talbot), pp. 261-289. Acad. Press, London, 1970. (MR 42, 751.)

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12. Chi, D. N.-H.

*

Linear multistep methods based on g-splines, (doctoral dissertation). University of Pittsburgh, 1970. (DA

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2812-B.)

13. Chu, S.C.

Piecewise polynomials and the partition method for nonlinear ordinary differential equations.

J. Engrg. Math.

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(1970), 65-76. (MR

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2933; Zb 208, P• 418.) 14. Ciarlet, P.G.; Varga, R.S.

Discrete variational Green's function. II: One dimensional problem. Numer. Math.

J!

(1970), 115-128. (CA

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825; BS 32, 1231.)

15. Covaci-Munteanu, M.J.

*

Contributions

a

la theorie des fonctions splines

a

une et

a

plusieurs variables.

Universite Catholique de Louvain. These. Louvain, 1970. 16. Curtis, A.R.

The approximation of a function of one variable by cubic splines. Numerical approximation to functions and data. Ed. by J.G. Hayes, pp. 28-42. Athlone Press, London, 1970. (CR ~' 20155.)

17. Douglas, J. jr.; Dupont, T.

Galerkin methods for parabolic equations. SIAM J. Numer. Anal.

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(1970), 575-626. 18. Freud, G.; Popov, V.A.

Some questions that are related to the approximation by spline func-tions and polynomials.

Studia Sci. Math. Hungar. 5 (1970), 161-171 (Russian). (MR 42, 2225; Zb 201, p. 396.)

19. Fyfe, D.J.

The use of cubic splines in the solution of certain fourth order boundary value problems.

Comput. J.

11

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il'

6407; Zb 191, p. 167; CA_!i, 2110.)