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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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MathSciNet review: 1567359
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Larry L. Schumaker
Title: Spline functions: Basic theory
Additional book information: Wiley, New York, 1981, xiv + 553 pp., $42.50.

References [Enhancements On Off] (What's this?)

1.
N. Achieser and M. Krein [1937], On the best approximation of periodic functions, Dokl. Akad. Nauk SSSR 15, 107-112.
  • J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The theory of splines and their applications, Academic Press, New York-London, 1967. MR 0239327
  • Carl de Boor, Bicubic spline interpolation, J. Math. and Phys. 41 (1962), 212–218. MR 158512
  • Carl de Boor, On local linear functionals which vanish at all $B$-splines but one, Theory of approximation, with applications (Proc. Conf., Univ. Calgary, Calgary, Alta., 1975; dedicated to the memory of Eckard Schmidt), Academic Press, New York, 1976, pp. 120–145. MR 0417628
  • Carl de Boor, A practical guide to splines, Applied Mathematical Sciences, vol. 27, Springer-Verlag, New York-Berlin, 1978. MR 507062
  • Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York, Inc., New York, 1967. MR 0230022
  • E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222517
  • C. K. Chui, P. W. Smith, and J. D. Ward, Favard’s solution is the limit of $W^{k,p}$-splines, Trans. Amer. Math. Soc. 220 (1976), 299–305. MR 422954, DOI 10.1090/S0002-9947-1976-0422954-0
  • R. Courant, Variational methods for the solution of problems of equilibrium and vibrations, Bull. Amer. Math. Soc. 49 (1943), 1–23. MR 7838, DOI 10.1090/S0002-9904-1943-07818-4
  • Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1963. MR 0157156
  • Jim Douglas Jr., Todd Dupont, and Lars Wahlbin, Optimal $L_{\infty }$ error estimates for Galerkin approximations to solutions of two-point boundary value problems, Math. Comp. 29 (1975), 475–483. MR 371077, DOI 10.1090/S0025-5718-1975-0371077-0
    • 12.
    J. Favard [1937], Sur les meilleure procédés d'approximation de certaines classes des fonctions par des polynômes trigonométriques, Bull. Sci. Math. 61, 209-224; 243-256.
  • J. Favard, Sur l’interpolation, J. Math. Pures Appl. (9) 19 (1940), 281–306 (French). MR 5187
  • Stephen D. Fisher and Joseph W. Jerome, Minimum norm extremals in function spaces, Lecture Notes in Mathematics, Vol. 479, Springer-Verlag, Berlin-New York, 1975. With applications to classical and modern analysis. MR 0442780
    • 15.
    M. Golomb [1962], Lectures on theory of approximation, Argonne National Laboratory.
    16.
    M. Golomb [1967], Splines, n-widths and optimal approximations, MRC Tech. Rpt. 784, Mathematics Research Center, Madison, Wisconsin.
  • Michael Golomb and Joseph Jerome, Equilibria of the curvature functional and manifolds of nonlinear interpolating spline curves, SIAM J. Math. Anal. 13 (1982), no. 3, 421–458. MR 653466, DOI 10.1137/0513031
  • Michael Golomb and Hans F. Weinberger, Optimal approximation and error bounds, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Publication of the Mathematics Research Center, U.S. Army, the University of Wisconsin, no. 1, University of Wisconsin Press, Madison, Wis., 1959, pp. 117–190. Edited by R. E. Langer. MR 0121970
  • Thomas N. E. Greville, The general theory of osculatory interpolation, Trans. Actuar. Soc. America 45 (1944), 202–265. MR 12917
  • T. N. E. Greville, Introduction to spline functions, Theory and Applications of Spline Functions (Proceedings of Seminar, Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1968) Academic Press, New York, 1969, pp. 1–35. MR 0240521
  • John C. Holladay, A smoothest curve approximation, Math. Tables Aids Comput. 11 (1957), 233–243. MR 93894, DOI 10.1090/S0025-5718-1957-0093894-6
  • Joseph W. Jerome, On the ${\cal L}_{2}\,n$-width of certain classes of functions of several variables, J. Math. Anal. Appl. 20 (1967), 110–123. MR 216225, DOI 10.1016/0022-247X(67)90111-4
    • 23.
    J. Kahane [1961], Teoria constructiva de functiones, University of Buenos Aires.
  • Samuel Karlin, Total positivity. Vol. I, Stanford University Press, Stanford, Calif., 1968. MR 0230102
  • Samuel Karlin, Charles A. Micchelli, Allan Pinkus, and I. J. Schoenberg (eds.), Studies in spline functions and approximation theory, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0393934
  • Samuel Karlin and William J. Studden, Tchebycheff systems: With applications in analysis and statistics, Pure and Applied Mathematics, Vol. XV, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1966. MR 0204922
  • B. S. Kašin, The widths of certain finite-dimensional sets and classes of smooth functions, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), no. 2, 334–351, 478 (Russian). MR 0481792
  • Donald E. Knuth, Mathematical typography, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 2, 337–372. MR 520078, DOI 10.1090/S0273-0979-1979-14598-1
    • 29.
    D. Knuth[1979b], Tex and metafont, (Part 3, pp. 20-21), Digital Press, North Billerica, Mass.
    30.
    A. Kolmogorov [1936], Annäherung von Funktionen einer gegebenen Funktionklasse, Ann. of Math. 31, 107-111.
    31.
    D. Knuth [1939], On inequalities between the upper bounds of the successive derivatives of an arbitrary function on an infinite interval, Amer. Math. Soc. Trans. Series 1, 2 (1962), 233-243.
  • G. G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, New York-Chicago, Ill.-Toronto, Ont., 1966. MR 0213785
  • Günter Meinardus, Approximation of functions: Theory and numerical methods, Expanded translation of the German edition, Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag New York, Inc., New York, 1967. Translated by Larry L. Schumaker. MR 0217482
    • 34.
    A. Melkman and C. Micchelli [1976], On non-uniqueness of optimal subspaces for L, IBM Res. Rpt. RC 6113, Yorktown Hts., N. Y.
    35.
    W. Quade and L. Collatz [1938], Zur Interpolationstheorie der reelen periodischen Funktionen, Akad. Wiss. 30, 383-429.
  • John R. Rice, The approximation of functions. Vol. I: Linear theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964. MR 0166520
  • Arthur Sard, Best approximate integration formulas; best approximation formulas, Amer. J. Math. 71 (1949), 80–91. MR 29283, DOI 10.2307/2372095
  • Arthur Sard, The rationale of approximation, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Publication of the Mathematics Research Center, U.S. Army, the University of Wisconsin, no. 1, University of Wisconsin Press, Madison, Wis., 1959, pp. 191–207. Edited by R. E. Langer. MR 0104334
  • Arthur Sard, Linear approximation, American Mathematical Society, Providence, R.I., 1963. MR 0158203
  • Arthur Sard and Sol Weintraub, A book of splines, John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0283961
    • 41.
    I. Schoenberg [1946], Contributions to the problem of approximation of equidistant data by analytic functions, Quart. Appl. Math. 4, 45-99 (Part A), 112-141 (Part B).
  • I. J. Schoenberg, Cardinal spline interpolation, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. MR 0420078
  • Martin H. Schultz, Spline analysis, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973. MR 0362832
  • Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973. MR 0443377
  • V. M. Tihomirov, Best methods of approximation and interpolation of differentiable functions in the space $C[-1,\,1].$, Mat. Sb. (N.S.) 80 (122) (1969), 290–304 (Russian). MR 0256043
  • A. F. Timan, Theory of approximation of functions of a real variable, A Pergamon Press Book, The Macmillan Company, New York, 1963. Translated from the Russian by J. Berry; English translation edited and editorial preface by J. Cossar. MR 0192238
  • Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
    •
    Review Information:

    Reviewer: Joseph W. Jerome
    Journal: Bull. Amer. Math. Soc. 6 (1982), 238-247
    DOI: https://doi.org/10.1090/S0273-0979-1982-14996-5