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van Rooij, P. L. J., & Schurer, F. (1973). A bibliography on spline functions II. (EUT report. WSK, Dept. of Mathematics and Computing Science; Vol. 73-WSK-01). Technische Hogeschool Eindhoven.
Document status and date: Published: 01/01/1973
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ONDERAFDELING DER WISKUNDE DEPARTMENT OF MATHEMATICS
A bibliography on spline functions. II by
P.L.J. van Rooij and F. Schurer
T.H.-Report 73-WSK-01 January 1973
Introduction
About one year ago we published a report* that contained a bibliography on spline functions. The compilation included three kinds of publications, namely, papers in mathematical periodicals, books, and doctoral disserta-tions, all of which had appeared before January 1, 1971. For various reasons a fourth kind of publication, reports, was not included in the bibliography. The report was sent to a number of mathematicians working in the field of spline approximation with a request to suggest corrections and improve-ments. As a result of that, we generously received a large number of comments on the report. Although it is impossible here to mention all those who re-sponded, we in particular want to thank B.I. Kvasov, G. Micula, J. Nitsche, K. Scherer, LJ. Schoenberg, L.L. Schumaker, E. Stark,and R.S. Varga for their contributions. Especially B.l. Kvasov supplied us with most useful information on spline papers written by Russian authors.
The present report is a revised and augmented version of the first edi-tion. To the best of our knowledge we included all papers, books and doctoral dissertations that appeared be~ore January 1,1972 and which deal with the theory and application of spline approximation. As before, reports were not included in the bibliography.
The main part of the report consists of a list ordered chronologically and, 'for publications that have appeared 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. Of course, the decision for in-cluding or not a particular publication was sometimes rather difficult and the outcome may be subject to criticism. In this respect we greatly valued all the advice we received concerning the contents of the bibliography, but we did not invariably follow it. Thus the responsibility for the omissions and errors in the present report is entirely ours, while the improvements are largely due to those who responded.
As we already remarked in the first version of the bibliography 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 [67-2J and l.n
the books edited by Grevillc 169-:321 and Schoenberg [69-86J, respectively.
OtlU.'l- lIseful information is contailled in tile btbliography "Recent
pUblica-tions 1n approximation tllcory willi l'lllpll:Jsis on computer. applications",
(;om-piled by C.L. Lawson . (Computing Reviews 9 (1968), 691-699). One may also consult the paper by Schultz and Varga [67-37]. In addition to these sources, we particularly want to call the reader's attention to the fine bibliography
1n the monograph of Sard and Weintraub [71-96J which recently appeared. The journal abbreviations are those given in Hathematical Reviews 41
(1971), 1939-1960. We have strived to add to each publication one or more references to reviews 1n Mathematical Reviews (MR), Zentralblatt fur Mathe-matik (Zb), Referativnyi 1urnal MateMathe-matika (RJH) , Computing Reviews (CR), Computer Abstracts eCA) , Bulletin Signaletique 110 CBS) and Dissertation Abstracts (DA). In comparison with the first version of the bibliography the references to reviews in the Referativnyi Zurnal Matematika are new. An asterisk
*
indicates that the publi is a doctoral dissertation,or a book that is mainly concerned with spline functions.The compilation contains a total number of 614 items, of which 532 have been published during the years 1966-1971. Although the bibliography is certainly not complete, we hope that it gives a reasonable survey of the existing literature on spline functions until January 1, 1972.
During the project Miss Yvonne Naus of the mathematics library of the Technological University Eindhoven has been of valuable assistance to us. It 18 a pleasure to thank her again for all the work she has done.
Finally, we convey our gratitude to Mrs. E.E.F.M. Baselmans~Weijers for her superb technical typing.
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p. 1 16. )1944 1. Love, A.E.R.
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une probleme d' interpolatio.n. C.R. Acad. Sci. Paris Sera A 228 (1949), "1996-1998 •. (ViR.!.!., p. 86.) -3. Synge, J.L.; Griffith, B.A.
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p. 83; Zb 39, p. 342.)2. Meyers, L.F.; Sard, A.
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p. 396; Zb 40, p. 28.)1953 1. Schoenberg, I.J.; Whitney, A.
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curves.
Trans. Amer. Math. Soc. 74 (1953), 246-259.
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I. ShaLdaeva, T.A.
*
Most precise quadrature formulae for certain classes of functions (Russian) (Doctoral dissertation).Leningrad State Univ., Leningrad, 1954. 1956
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1957 1. Holladay, J.C.
A smoothest curve approximation.
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2. Ionescu, D.V.
Numerical quadrature (Roumanian). Editura Tehnica, Bucure~ti, 1957. 1958
"
I. Nikolskii, S.M.
Quadrature formulae (Russian). Moscow, 1958.
'Translated as International monographs on advanced mathematics and physics, no. 29.
Rindustan Publ. Corp., Delhi (India), 1964. 2. Schoenberg, I.J.
Spline functions, convex curves and mechanical quadrature. Bull. Amer. Math. Soc. 64 (1958), 352-357.
(MR 20, 7174; Zb 85, p.~37; RJM (1959), 10957.) 1959
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-3. Golomb, M.; Weinberger, R.F.
Optimal approximation and error bounds.
in: 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 92, p. 58; RJM (1960), 12183.) 4. Krylov, V. 1.
v
Approximate calculation of integrals (Russian). Gos. Izdat. Fiz.-Mat. Lit. Mosk., 1959.
(MR 22, 2002.)
Translated at Macmillan. New York, 1962. (MR~, 2008.)
5. Shaidaeva, T.A.
Quadrature formulae with least error estimate for some classes of func-tions (Russian).
Trudy Mat. Inst. Steklov 53 (1959), 313-341. (MR~, 200 I • )
6. Simonsen, W.
On numerical differentiation of functions of several variables. Skand. Aktuarietidskr. 42 (1959), 73-89.
--1960
I. Birkhoff, G.; Garabedian, H.L. Smooth surface interpolation.
J. Math. and Phys. 39 (1960), 258-268.
(MR~, 10151; Zb 161, p. 129; RJM (1962), 6VI88.) 2. Ciesielski, Z.
On the isomorphisms of the spaces Ha and m.
Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.
!
(1960), 2]7-222. (MR 24, A2234; Zb 93, p. 123; RJM (1961), 7B413.)3. Ciesielski, Z.
Some properties of Schauder bases of the space C[O,I].
Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.
!
(1960), 141-144. (MR 26, 5417; Zb21,
p. 70; RJM (1961), 4BI2.)4. Johnson, R.S.
On monosplines of least deviation.
Trans. Amer. Math. Soc. 96 (1960), 458-477. (HR 23, A270; RJM (1963)-, 4BIOI.)
5. Rutishauser, H.
Bemerkungen zur glatten Interpolation. Z. Angew. Math. Phys. II (1960), 508-513.
(MR 26, 883; RJM (1961~ 12V311.) 6. Schwerdtfeger, H.
Notes on numerical analysis. II: Interpolation and curve fitting by sectionally linear functions.
Canad. Math. Bull. 3 (1960), 41-57. (Zb 96, p. 103; RJM-(I961), 8V245.)
1961
"
I. Brudny~, Yu.A.; Gopengauz, I.E.
Approximation by piecewise polynomial functions.
Dokl. Akad. Nauk SSSR ~ (1961), 1283-1286 (Russian). Translated as Soviet Math. Dokl. 2 (1961), 1627-1630.
(MR 24, A2175; RJM (1962), 9B82.)-2. Schwerdtfeger, H.
Notes on numerical analysis. III: Further remarks on sectionally linear functions.
Canad. Math. Bull. 4 (1961), 53-55. (Zb 106, p.109; RJM-(1962), 4V191.) 3. Theilheimer, F.; Starkweather, W.
The fairing of ship lines on a high-speed computer. Math. Compo 15 (1961), 338-355.
(MR~, B1627; Zb 109, p. 350; RJM (1962), IIVI80.) 4. Weinberger, H.F.
Optimal approximation for functions prescribed at equally spaced points. J. Res. Nat. Bur. Standards Sect. B 65 (1961), 99-104.
1962
1. Asker, B.
The spline curve, a smooth interpolating function used in numerical design of ship-lines.
BIT 2 (1962), 76-82. (Zb lIZ, p. 81.) 2. Boor, C. de
Bicubic spline interpolation.
J. Math. and Phys. 41 (1962), 212-218.
(MR 28, 1735; Zb 108, p. 271; RJM (1963), 6V48.) 3. Landis, F.; Nilson, E.N.
The determination of thermodynamic properties by direct differe~tiation techniques.
in: Progress in international research on thermodynamic and transport properties (Second Symp. on Thermophysical Properties); 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 Ge~man summaries) •
Eesti NSV Tead. Akad. Toimetised Fuus.-Mat. 11 (1962), 24-32. (MR 25, 3307; RJM (1963), IBI02.)
5. Walsh, J.L.; Ahlberg, J.H.; Nilson, E.N.
Best approximation properties of the spline t. J. Math. Mech. 1 J (1962), 225-234.
(MR 25, 738; Zb 196, p. 486; RJM (1963), 5BI12.) 1963
1. Ahlberg, J.H.; Nilson, E.N.
Convergence properties of the spline fit. J. Soc. Indust. Appl. Math. 11 (1963), 95-104.
(MR~, 2763; Zb 196, p. 487;-RJM (1964), 1B574.) 2. Berger, S.A.; Webster, W.C.
An application of linear programming to the fairing of ships' lines. in: Recent advances in mathematical programming; ed. by R.L. Graves and P. Wolfe, pp. 241-253.
McGraw-Hill, New York, 1963. 3. Boor, C. de
Best approximation properties of spline functions of odd degree. J. Math. Mech. 12 (1963), 747-749.
(MR~, 398Z; Z~116, p. 276; RJM (1965), 3BI51.)
v
4. Brudny~, Yu.A.; Gopengauz, I.E.
Approximation by piecewise polynomial functions (Russian). Izv. Akad. Nauk SSSR Ser. Mat. 27 (1963), 723-746.
(MR 29, 404; RJM (1964), 4B92.)-5. Ciesielski, Z.
Properties of the orthonormal Franklin system. Studia Math. 23 (1963), 141-157.
6. Sard, A.
Linear approximation.
Amer. Math. Soc.~Providence (R.I.), 1963.
(MR 28, 1429; Zb ~, p. 54; RJM (1965), 7B88.) 7. Schaefer, H.
Latteninterpolation bei einer Funktion von zwei Veranderlichen. Z. Angew. Math. Phys. 14 (1963), 90-96.
(Zb 108, p. 300; RJM (1963), IIVI03.) 1964 1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.
Fundamental properties of generalized splines. Proc. Nat. Acad. Sci. USA 52 (1964), 1412-1419.
(MR 36, 6846; Zb 136, p. 362; RJM (1965), I2B472; BS 26, 9981.) 2. Ahlin, A.C.
A bivariate generalization of Hermite's interpolation formula. Math. Compo 18 (1964), 264-273.
(MR~, 1725;Zb 122, p. 125; RJM (1964), JOB463.) 3. Birkhoff, G.; Boor, C. de
Error bounds for spline interpolation. J •. Math. Mech. 13 (1964), 827-835.
(MR~, 2583; Zb 144, p. 285; RJM (1965), 8B93; BS 26, 6171.) 4. Ciesielski, Z.
On the orthonormal Franklin system.
Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 12 (1964), 461-464.
(MR 29, 6241; Zb 138, p. 50; RJM (1965), 7B417.) 5. Ferguson, J.
Multivariahle curve interpolation.
J. Assoc. Comput. Mach. 11 (1964), 221-228.
(MR 28, 5551; Zb 123, p.~30; RJM (196$), 4B738; CA~, 1806.) 6. Greville, T.N.E.
Numerical procedures for interpolation by spline functions.
SIAM .T, Num~r, Anal. 1 0.964), 53-68. (MR 36, 4784; Zb ~,-p. 336.)
7. Mehlum, E.
A curve-fitting method based on a variational criterion. BIT 4 (1964), 213-223.
(MR 30, 4376; RJM (1965), 9B330.) 8. P~vlHob, I.
Sur l'interpolation
a
l'aide de polynomes raccordes. Mathematica (Cluj) 6 (1964), 295-299.(RJM (1966), 9B634.) 9. Podolsky, B.; Denman, H..H.
Conditions on minimization criteria for smoothing. Math. Compo 18 (1964), 441-448.
10. Schechter, E.
Error estimation by means of differential inequalities. Mathematica (Cluj) 6 (1964), 117-128.
(Zb 221, 65119; RJM-(l966) , 12B492; BS
'!:2,
6082.) 11. Schoenberg, I.J.Spline interpolation and best quadrature formulae. Bull. Amer. Math. Soc. 70 (1964), 143-148.
(MR~, 394; Zb 136, p.:362; RJM (1964), IIB99.) 12. Schoenberg, I.J.
Spline interpolation and the higher derivatives. Proc. Nat. Acad. Sci. USA 51 (1964), 24-28.
(MR 28, 3278; Zb 136, p. 362; RJM (1965), 6BI16.) 13. Schoenberg, I.J.
On best approximation of linear operators.
Nederl. Akad. Wetensch. Proc. Ser. A 67 (1964), 155-163. (MR 28, 4284; Zb 146, p. 85; RJM (1965), IB93.)
14. Schoenberg, I.J.
On trigonometric spline interpolation. J. Math. Mech. 13 (1964), 795-825.
(MR~, 2589; Z~147, p. 321; RJM (1965), 8B92; BS ~, 6179.) 15. Schoenberg, I.J.
Spline functions and the problem of graduation. Proc. Nat. Acad. Sci. USA 52 (1964), 947-950.
(MR 29, 5040; Zb 147, p. 321; RJM (1965), 8B502; BS ~, 6175.) 16. Schoenberg, I.J.
On interpolation by spline functions and its minimal properties.
in: On approximation theory (Proc. Conf. Oberwolfach, Aug. 1963); ed. by P.L. Butzer and J. Korevaar, pp. 109-129.
Birkhauser Verlag, Basel, 1964.
(MR
l!,
5015; Zb 147, p. 321; RJM (1966), 6B130; BS 26, 11449.) 17. Smoluk, A.On the approximation with piecewise functions (Polish).
Zeszyty Nauk. Wyz. Szkol. Ekon. Wroclawiu (1964), no. 21, 107-121. (RJM (1968), 2BI49.)
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; Z~141, p. 68; RJM (1966), IB116; BS 26, 13312.) 2. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L.
Convergence properties of generalized splines. Proc. Nat. Acad. Sci. USA 54 (1965), 344-350.
(MR 36, 6847; Zb 136, p. 363; RJM (1966), 7BI58; BS
'!:2,
4501.) 3. MIlberg, J.H.; Nilson, E.N.Orthogonality properties of spline functions~
J. Math. Anal. Appl. II (1965),321-337.
4. Ahlberg, J.R.; Nilson, E.N.; Walsh, J.L.
Extremal, orthogonality, and convergence properties of multidimensional splines.
J. Math. Anal. Appl. 12 (1965), 27-48.
(MR
1I,
661; Zb 136, ~ 48; RJM (1966), 7BI57.) 5. Atteia, M.Gen&ralisation de la definition et des proprietes des "spline fonctions". C.R. Acad. Sci. Paris Sere A 260 (1965), 3550-3553.
(MR~, 3340; Zb 163, p. 377; RJM (1966), IB636; BS~, 10401.) 6. Atteia, M.
"Spline-fonctions" generalisees.
C.R. Acad. Sci. Paris Sere A 261 (1965), 2149-2152. (MR 35, 3341; RJM (1966), 9B517; BS ~, 2127.) 7. Birkhoff, G.; Boor, C.R. de
Piecewise polynomial interpolation and approximation.
in: Approximation of functions (Proc. Symp. on Appr. Functions, Gen. Motors Res. Lab., Warren, Michigan, 1964); ed. by R.L. Garabedian, pp.
!64-190. Elsevier, Amsterdam, 1965.
(MR 32, 6646; Zb 136, p. 47; BS ~, 7289.) 8. Collatz, L.
Einschliessungssatz fur die Minimalabweichung bei der Segmentapproxima-tion.
in: Simposio internazionale sulle applicazioni dell' Analisi alIa Fisica Matematica (Cagliari-Sassari, 1964), pp. 11-21. Cremonese, Rome, 1965. (MR35, 633; Zb 221,65020; RJM (1967), 2B583.)
9. Glass, J.M.
*
A criterion for the quantization of line-drawing data (Doctoral disser-tation).New York Univ., Bronx, 1965. 10. Kirishchiev, R.I.; Neshevich, D.A.
Some problems concerning the interpolation of functions (Russian).
U~en. Zap. Kabard.-Balkar. Gos. Univ. Sere Fiz.-Mat. 24 (1965), 113-119. (RJM (1967), 5B707.)
11. Schoenberg, I.J.
On monosplines of least deviation and best quadrature formulae. SIAM J. Numer. Anal. 2 (1965), 144-170.
(HR 34, 2182; Zb 136,-p. 362; RJM (1966), 9B610; BS ~, 2149.) 12. Secrest, D.
Numerical integration of arbitrarily spaced data and estimation of errors.
SIAM J. Numer. Anal. 2 (1965), 52-68.
(MR
ll,
4176; Zb 135,-p. 386; RJM (1966), 7B532; BS ~, 2122.) 13. Secrest, D.Best approximate integration formulas and best error bounds. Math. Compo 19 (1965), 79-83.
(MR 33, 196i";Zb 134, p. 136; RJM (1966), IB569; CA~, 831; BS~, 10411.) 14. Secrest, D.
Error bounds for interpolation and differentiation by the use of spline functions.
SIAM J. Numer. Anal. 2 (1965), 440-447.
15. Subbotin, Yu.N •.
On the relations between finite differences and the corresponding derivatives.
Trudy Mat. lnst. Steklov 78 (1965), 24-42 (Russian). Translated as Extremal properties of polynomials; ed. by S.B. Ste~kin (Proc. Steklov Inst. Math. 78 (1965», pp. 23-42. Amer. Math. Soc., Providence, .] 967.
-(MR 32, 7978; RJM (1966), 3BI59.) 16. Tihomirov, V.M.
Sor,le problems of approximation theory.
Dokl. Akad. Nauk 160 (1965), 774-777 (Russian). Translated as Soviet Math. Dokl. 6 (1965), 202-205.
(RJM(l965), 7B80.)
-17. Wendroff, B.
Bounds for eigenvalues of some differential operators by the Rayleigh-Ritz method.
Math. Compo 19 (1965), 218-224.
(MR
2l,
4J69;-RJM (1966), IB543; BS~, 13893.) 19661. Ahlberg, J.H.; Nilson, E.N.
The approximation of linear functionals. SIAM J. Numer. Anal. 3 (1966), 173-182.
(MR 36, 589; Zb 147,
p.
51; RJM (1967), 7B510.) 2. Atteia, M.*
Etude de certains noyaux et theorie des fonctions "spline" en Analyse Numerique (These).Universite de Grenoble, Grenoble, 1966. (BS ~, 6564.)
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; Zb 168, p. 350; RJM (1967), 8B478; BS ~, 8613.) 4. Aubin, J.P.
*
Approximation des espaces de distributions et des operateurs differen-tiels (These Doct. Sci. Math.).Universite de Paris, Paris, 1966. (BS~, 16561.)
5. Barrodale, I.; Young, A.
A note on numerical procedures for approximation by spline functions. Comput. J. 9 (1966), 318-320.
(MR 34, 21ST; Zb ]68, p. ]49; RJM (1967), 5B709; CA
ll,
69; BS 28, 6535.) 6. Berger, S.A.; Webster,w.e.;
Tapia, R.A.; Atkins, D.A.Mathematical ship lofting.
J. Ship Research ~ (1966), 203-222.
7. Birkhoff, Go; Boor, C. de; Swartz, B.; Wendroff, B.
Rayleigh-Ritz approximation by piecewise cubic polynomials. SIAM J. Numer. Anal. 3 (1966), 188-203.
8. Birman,
M.S.;
Solomjak, M.Z.(l
Approximation of the functions of the classes Wp by piecewise polynomial functions.
Dokl. Akad. Nauk SSSR
lL!
(1966), 1015-1018 (Russian). Translated as Soviet Math. Dokl. 7 (1966), 1573-1577.ViR
35, 630; RJM (1967), 5BI20; BS-28, 7608.) 9. Boor, C. de*
The method of projections as applied to the numerical solution of two point boundary value problems using cubic splines (Doctoral dissertation). Univ. of Michigan, Ann Arbor, 1966.(BS~, 10097; DA~, 3592-B.) 10. Boor, C. de; Lynch, R.E.
On splines and their minimum properties.
J. Math. Mech. 15 (1966), 953-969. (MR 34, 3159; Z~185. p. 205.) II. Carasso, C.
*
Methodes numeriques pour l'obtention de fonctions-spline (These). Universite de Grenoble, Grenoble, 1966.(BS 28, 6538.) 12. Ciarlet, P.G.
*
Variational methods for nonlinear boundary value problems (Doctoral dissertation).Case Institute of Technology, Cleveland, 1966. (RS ~, 6141; DA~, 2437-B.)
13. Ciesielski, Z.
Properties of the orthonormal Franklin system, II.
Studia Math. 27 (1966), 289-323.
(MR 34, 3202;:Zb 148, p. 47; RJM (1967), 8B75.) 14. Coatmelec, C.
Approximation et interpolation des fonctions differentiables de plusieurs . variables.
Ann. Sci. Ecole Norm. Sup. 83 (1966), 271-341. (MR38, 469; RJM (1968), IIB94.)
IS. Coatmelec, C.
*
Approximation et interpolation des fonctions differentiables de plusieurs variables (These Doct. Sci. Math.).Universite de Rennes, Rennes, 1966.
(RJM (1969), 2B135; BS 29, 978.) 16. Curry, H.B.; Schoenberg, I.J.
On P6lya frequency functions. IV: The fundamental spline functions and their limits.
J. Analyse Math. 17 (1966), 71-107.
(MR~, 1884; Zb 146, p. 84; RJM (1967), 11B94; BS 28, 3756.) 17. Ehrich, H.
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(Zb T73, p. 186; RJM (1967), 9B619; CR~, 12801.) 19. Hands comb , D.C.
Spline functions.
in: Methods of numerical approximation; ed. by D.C, Handscomb, pp. 163-167. Pergamon Press, Oxford, 1966.
20. Hands comb , D.C.
Optimal approximation by means of spline functions.
in: Methods of numerical approximation; ed. by D.C. Hands comb , pp, 177-181. Pergamon Press, Oxford, .1966.
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Optimal approximation of linear functionals.
in: Methods of numerical approximation; ed. by D.C. Handscomb, pp. 169-176. Pergamon Press, Oxford, 1966.
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An example of precise interpolation with a spline function.
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(CR~, 12789; CA Q, 71-:-) 23. Karlin, S.; Studden, W.J.
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Chebyshevian spline functions.
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(MR~, 7041; Zb ~,-p. 310; RJM (1967), 8B603.) 25. Malozemov, V.N.
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(MR 35, 4648; Zb 17T, p. 310; RJM (1968), 6B142.) 27. Milnes, H.W.
A variational approach to smoothing unequally spaced data subject to random errors.
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On Hermite-Birkhoff interpolation.
J. Math. Anal. Appl. 16 (1966), 538-543.
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(HI{ 34,3170; Zb 147,-p. 321; RJM (1967), IIB658.)
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*
On some approximation problems involving Tchebycheff systems and spline functions (Doctoral dissertation).Stanford Univ., Stanford, 1966.
(RJM (1967), 9B106; BS .?2.., 2535; DA
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The spline in tension (hyperbolic spline) and the reduction of extraneous inflection points (Doctoral dissertation).Brown Univ., Providence, 1966. (DA 28, 267-B.)
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An interpolation curve using a spline in tension. J. Math. and Phys. 45 (1966), 312-317.
(MR 34, 6990; Zb 146, p. 141; RJM (1967), 9B617; BS 28, 7843.) 33. Sharma, A.; Meir, A.
Degree of approximation of spline interpolation. J. Math. Mech. 15 (1966), 759-767.
(MR 33, 3006; Z~158, p. 307; BS 28, 706.) 34. Stern, M.D.
*
Some problems in the optimal approximation of bounded linear functionals (Doctoral dissertation).Oxford Univ., Oxford, 1966. 35. Varga, R.S.
Hermite interpolation-type Ritz methods for two-point boundary value problems.
in: Numerical solution of partial differential equations (Proc. Symp. Univ. Maryland, 1965); ed. by J.H. Bramble, pp. 365-373.
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Complex cubic splines.
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(MR~, 573; RJM (1968),-gB764; BS.?2.., 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; BS .?2.., 976.) 3. Atteia, M.
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in: Actes du 5e Congres de l'AFIRO (Lille, 1966), pp. 113-116. Assoc. Fran~. d'Inform. et de Rech. Operat., Paris, 1967. 4. Atteia, M.
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5. Aubin, J.P.
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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. Bel'tjukov, B.A.
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Local spline approximation by moments. J. Math. Mech. 16 (1967),987-990.
(XR 34, 8051; Z~148, p. 292; RJM (1968), 7B84; BS 28, 13457.) 10. Birkhoff, G.; Priver, A.
Hermite interpolation errors for derivatives. J. Math. and Phys. 46 (1967), 440-447.
(MR~, 1883; Zb 176, p. 142; RJM (1968), 9B763, BS~, 11982.) II. Birman, M.S.; Solomjak, M.Z.
Piecewise-polynomial approximations of functions of the classes W~. Mat. Sb. 73 (1967), no. 3, 331-355 (Russian).
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Obtention d'une fonction-Spline d'interpolation d'ordre K par une methode d'integration locale.
in: Procedures Algol en Analyse Numerique I, pp. 288-291. Centre National de la Recherche Scientifique, Paris, 1967. 13. Carasso, C.
Methode pour l'obtention de fonctions-spline d'interpolation d'ordre deux.
in: Procedures Algol en Analyse Numerique I, pp. 292-294. Centre National de la Recherche Scientifique, Paris, 1967. 14. Carasso, C.
Obtention d'une fonction lisse passant par des points donnes et ayant en ces points des derivees donnees (fonction-spline d'Hermite).
ia: Procedures Algol en Analyse Numerique I, 295-299. Centre National de la Recherche Scientifique, Paris, 1967.
15. Car,lsso, C.
Obtention de lu d~riv6e d'une fanction donnie par points. in: Prol'cdurL'l'l Algol en Analyse Numerique 1, pp. 300-)01. Centre National de la Recherche scientifique, Paris, 1967. 16. Carasso, C.
Construction numerique de fonctions-spline.
in: Actes de 5e Congres de l'AFIRO (Lille, 1966), pp. 506-509. Assoc. Fran~. d'Inform. et de Rech. Operat., Paris, 1967. 17. Carasso, C.
Methode generale de construction de fonctions spline.
Rev. Fran~aise Informat. Recherche Operationnelle 1 (1967), no. 5, 119-127. (MR,R, 667; Zb 163, p. 377; RJM (1968), 10B860; BS 29, 13887.)
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Numer. Math. 9 (1967), 394-430.
(UR 36, 4813;-Zb 155, p. 204; RJM (1968), 4B751; BS 28, 14094.) 19. Cybertowicz, Z.
On some approximation problems.
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Lissage par utilisation de fonctions analogues aux fonctions spline. in: Actes du 6e Congres de l'AFIRO (Nancy, 1967), pp. 14-31.
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On the normalization of the B-splines and the location of the nodes for the case of unequally spaced knots.
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Utilisation des fonctions spline pour Ie lissage.
in: Actes du 5e Congres de l'AFIRO (Lille, 1966), pp. 349-352. Assoc. Fran~. d'Inform. et de Rech. Operat., Paris, 1967. 24. Joly, J.L.
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Bull. Amer. Math. Soc. 73 (1967), 438-442.
(MR~, 1218; Zb 1LL, p-.-363; BS ~, 4318.) 28. Loscalzo, F.R.; Talbot, T.D.
Spline function approximations for solutions of ordinary differential equations.
SIAM J. Numer. Anal. 4 (1967), 433-445.
(MR 36, 4808; Zb 1LL,-p. 363; RJM (1971), 3B588; CA
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Mat. Zametki I (1967), 537-540 (Russian). Translated as-Math. Notes I (1967), 355-357.
(MR 35, 5816; RJM (1968), TB145; BS 28, 13482.) 30. Meinguet, J.
Optimal approximation and error bounds in seminormed spaces. Numer. Math. 10 (1967), 370-388.
(MR
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(MR 36, 1887; Zb 1LL, p. 373; RJM (1968), 5B820; CA
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&1 application of monotone operators to differential and partial differ-ential equations on iftfinite domains (Doctoral dissertation).Case Institute of Technology, Cleveland, 1967. 33. Reinsch, C.H.
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(Zb ~, p. 362; RJM (1968), 6B850; CR~, 14528; BS ~, 8230.) 34. Rice, J.R.
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(MR 35, 3885; RJM (1969), 8B748; CA
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(MR~, 4645; Zb 159, p. 84; RJM (1967), 10B142; BS 28, 11774.) 42. Subbotin, Yu.N.
Interpolation by functions with nth derivative of minimum norm. Trudy Mat. lnst. Steklov 88 (1967). 30-60 (Russian).
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--(RJM (1968), 8B93; BS ~, 4270.) 43. Young, J.D.
Numerical applications of cubic spline functions. The Logistics Review 3 (1967), no. 14, 9-14.
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J. Approximation Theory 1 (1968), 5-)0. (MR 37, 6650; Zb 179, p.-365.)
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5. Anselone, P.M.; Laurent, P.J.
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(MR 37, 1853; Zb 208,-p. 408; RJM (1971), 4BI000j CR..!..!., 18292; BS 29, 17087.)
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Fonctions "spline" definies sur un ensemble convexe. Numer. Math. 12 (1968), 192-210.
(MR 41, 2265;:Zb 186, p. 452; RJM (1969), 4B659; CR~, 21056; BS 30, 6605.)
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(MR 37, 6651; RJM (1969), 7BI02; BS 30, 6358.) 9. Aubinp J.P.
Best approximation of linear operators in Hilbert spaces. SIAM J. Numer. Anal. 5 (1968), 518-521.
(MR 38, 6743; Zb 176,-p. 131; RJM (1971), 3B434; BS 30, 12694.) 10. Bickley, W.G.
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(MR 37, 6036; Zb 155, p. 480; RJM (1969), 2B790; CA~, 2551; BS 30, 5010.)
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Piecewise Hermite interpolation in one and two variables with appplica-tions to partial differential equaappplica-tions.
Numer. Math. 11 (1968), 232-256.
(MR 37, 2404;:Zb 159, p. 209; RJM (1968), 11B732; CA~, 2291; BS 29, 17158.)
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(MR 38, 4055.)
J 3. Boor, C. de
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14. Boor, C. de
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(MR 38, 869; Zb 159, p. 117; RJM (1969), 2B794; BS 30, 14610.) 22. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S.
Numerical methods of high-order accuracy for nonlinear boundary value problems. I I : Nonlinear boundary conditions.
Numer. Math. 11 (1968), 331-345.
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Numerical methods of high-order accuracy for nonlinear boundary value
p~oblems. III: Eigenvalue problems.
Numer. Math. 12 (1968), 120-133.
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Numer. Math. 12 (1968), 266-279.
(HR 39, 2337;Zb 181, p. 183; RJM (1969), 4B609; CR.!.!.., 19297; BS 30, 10923.)
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Numerical methods of high-order accuracy for nonlinear two-point boundary value problems.
in: Programmation en Mathematique Numerique (ColI. Intern. CNRS, no. 165, Besan~on, 1966), pp. 217-22S.
Centre National de la Recherche Scientifique, Paris, 1968.
(MR 38, 1837; Zb 207, p. 164; RJM (1968), 12B768; BS~, 17160.) 26. Ciesielski, Z.
A bounded orthonormal system of polygonals. Studia Math. 31 (1968), 339-346.
(MR 38, 3686;:Zb 169, p. 402; RJM (1969), 9B83.) 27. Cybertowicz, Z.
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(MR 38, 2496; RJM (1969), SB76S; BS 30, 8117.)
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29.
Interpolation, derivation et integration
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C.R. Acad. Sci. Paris Ser A 267 (1968), 309-312. (MR 40, 4652; RJM (1969), SB642.)
30. Einarsson, B.
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(MR 39, 1114; Zb 187, p. 105; RJM (1969), 9BS69; CR!Q, 17886; CA~, 542.) 31. El Tom~ M.E.A.
*
Numerical approximation of functions of one or more variables (Doctoral dissertation).Oxford Univ., Oxford, 1968. 32. Fix, G.
*
Bounds and approximations for eigenvalues of self-adjoint boundary value problems (Doctoral dissertation).Harvard Univ., Cambridge (Mass.), 1968. 33. Forrest, A.R.
*
Curves and surfaces for computer aided design (Doctoral dissertation). Cambridge Univ., Cambridge, 1968.34. Golomb, M.
Approximation by periodic spline interpolants on uniform meshes.
J. Approximation Theory 1 (1968), 26-6S.
(MR 38, 1444; Zb 18S, p.-309.) 35. Hall, C.A.
. On error bounds for spline interpolation. J. Approximation Theory 1 (1968), 209-218.
36. Herbold, R.J.
*
Consistent quadrature schemes for the numerical solution of boundary value problems by variational techniques (Doctoral dissertation). Case Western Reserve Univ., Cleveland, 1968.(CR,2., 15006; DA 30, 165-B.)
37. Horsley, A.; Parker, J.B.; Parker, K.; Price, J.A.
Curve fitting and statistical techniques for use in the mechanized evaluation of neutron cross sections.
Nuclear Instruments and Methods ~ (1968), 29-42.
38. Hulme~ B.L.
Interpolation by Ritz approximation.
J. Math. Mech. 18 (1968), 337-341.
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in: Latvian Math. Yearbook, Vol. 4, pp. 149-163. 17.dat. "Zinatne", Riga, 1968.
(MR~, 2293; Zb 208, p. 409.) 40. 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; RJM (1971), 4BI001; BS 30, 14544.) 41. Johnson,
a.G.
*
Convergence, error bounds, sensitivity, and numerical comparisons of certain absolutely continuous Rayleigh-Ritz methods for Sturm-Liouville eigenvalue problems (Doctoral dissertation).Univ.of California, Berkeley, 1968. (DA~, 3396-B.)
42. Karlin, S.
'Cotal positivity, Vol. }. pp. 357-364; pp. 501-564. Stanford Univ. Press, Stanford, 1968.
(MR
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(MR 38, 3664; Zb 165, p.-386.) 44. Karon, J.M.
* The sign-regularity properties of a class of Green's functions for ord.inary differential equations and some related results (Doctoral dissertation).
Stanford Univ., Stanford, 1968. (RJM (1969), 12B300; DA~, 2529-B.)
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Representation de donnees experimentales
a
l'aide de fonctions-spline d'ajustement et evaluation optimale de fonctionnelles lineaires conti-nues.ApI. Mat. 13 (1968),154-162.
46. Laurent, P.J.
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*
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.)
48~ Marsden, M.J.
*
An identity for spline functions with applications to variation-dimin-ishing spline approximation (Doctoral dissertation).Univ. of Wisconsin, Madison, 1968. (DA 29, 2985-B.)
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One-sided spline approximation.
Studia Sci. Math. Hungar. 3 (1968), 211-218.
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Convergence of a class of interpolatory splines. J. Approximation Theory I (1968), 243-250.
(MR 38, 3665; Zb 186, p.-114.) 51. Munteanu, M.J.
Observations on the optimal solution of a nonlinear differential boundary value problem in the subspace of generalized spline functions (Roumanian). Bul. sti. lnst. Politehn. Cluj 11 (1968), 47-56.
(MR 40, 7522.)
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On a method to approximate signals (Russian). Avtomatika (Kiev) ~ (1968), 75-80.
53. Phillips, G.M.
Algorithms for piecewise straight line approximations. Comput. J. ] 1 (1968), 21 ]-212.
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2529; BS 30, 4927.) 54. Powell, M.J.D.On best L2 spline approximations.
in: Numerische Mathematik, Differentialgleichungen, Approximationstheorie (Proc. Conf. Oberwolfach, 1966); hrsg. von L. Collatz, G. Meinardus und H. Unger, pp. 317-339.
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*
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*
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*
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