Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Retrieve article in: PDF

Book Information

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


References:

1.
N. Achieser and M. Krein [1937], On the best approximation of periodic functions, Dokl. Akad. Nauk SSSR 15, 107-112.
2.
J. Ahlberg, E. Nilson and J. Walsh [1967], The theory of splines and their applications, Academic Press, New York. MR 239327
3.
C. deBoor [1962], Bicubic spline interpolation, J. Math. Phys. 12, 747-749. MR 158512
4.
C. deBoor [1976], On local linear functional which vanish at all B-splines but one, Theory of Approximation, with Applications (Law and Sahney, eds. ), Academic Press, New York, pp. 120-145. MR 417628
5.
C. deBoor[1978], A practical guide to splines, Springer-Verlag, New York. MR 507062
6.
P. Butzer and H. Berens [1967], Semi-groups of operators and approximation, Springer-Verlag, Berlin. MR 230022
7.
E. Cheney [1966], Introduction to approximation theory, McGraw-Hill, New York. MR 222517
8.
C. Chui, P. Smith and J. Ward [1976], Favard's solution is the limit of W, Trans. Amer. Math. Soc. 220, 299-305. MR 422954
9.
R. Courant [1943], Variational methods for the solution of problems of equilibrium and vibration, Bull. Amer. Math. Soc. 49, 1-23. MR 7838
10.
P. Davis [1963], Interpolation and approximation, Blaisdell, New York. MR 157156
11.
J. Douglas, T. Dupont and L. Wahlbin [1975], Optimal L, Math. Comp. 29, 475-483. MR 371077
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.
13.
J. Favard[1940], Sur l'interpolation, J. Math. Pures Appl. 19, 281-306. MR 5187
14.
S. Fisher and J. Jerome [1975], Minimum norm extremals in function spaces, Lecture Notes in Math., no. 479, Springer-Verlag, Berlin. MR 442780
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.
17.
M. Golomb and J. Jerome [1979], Equilibria of the curvature functional and manifolds of nonlinear interpolating spline curves, MRC Tech. Rpt. 2024, Mathematics Research Center, Madison, Wisconsin. Also, SIAM J. Math. Anal., 1982. MR 653466
18.
M. Golomb and H. Weinberger [1959], Optimal approximation and error bounds, On Numerical Approximation (R. Langer, ed. ), University of Wisconsin Press, pp. 117-190. MR 121970
19.
T. Greville [1944], The general theory of osculatory interpolation, Trans. Actuar. Soc. Amer. 45, 202-265. MR 12917
20.
T. Greville[1969], Theory and applications of spline functions, Academic Press, New York. MR 240521
21.
J. Holladay [1957], A smoothest curve approximation, Math Tables Aids Computation 11, 233-243. MR 93894
22.
J. Jerome [1967], On the L, J. Math. Anal. Appl. 20, 110-122. MR 216225
23.
J. Kahane [1961], Teoria constructiva de functiones, University of Buenos Aires.
24.
S. Karlin [1968], Total positivity, Stanford University Press. MR 230102
25.
S. Karlin, C. Micchelli, A. Pinkus and I. Schoenberg [1976], Studies in spline functions and approximation theory, Academic Press, New York. MR 393934
26.
S. Karlin and W. Studden [1966], Tchebycheff systems with applications in analysis and statistics, Wiley Interscience, New York. MR 204922
27.
B. Kašin [1977], The widths of certain finite dimensional sets and classes of smooth functions, Izv. Akad. Nauk. SSSR Ser. Mat. 11, 334-351. MR 481792
28.
D. Knuth [1979a], Mathematical typography, Bull. Amer. Math. Soc. (N. S. ) 1, 337-372. MR 520078
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.
32.
G. Lorentz [1966], Approximation of functions, Holt, Rinehart and Winston, New York. MR 213785
33.
G. Meinardus [1967], Approximation of functions: Theory and numerical methods, Springer-Verlag, Heidelberg. MR 217482
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.
36.
J. Rice [1964], The approximation of functions, Vol. 1, Linear Theory, Addison-Wesley, Reading, Mass. MR 166520
37.
A. Sard [1949], Best approximate integration formulas, best approximation formulas, Amer. J. Math. 71, 80-91. MR 29283
38.
A. Sard [1959], The rationale of approximation, On Numerical Approximation (R. Langer, ed. ), University of Wisconsin Press, pp. 191-207. MR 104334
39.
A. Sard [1963], Linear approximation, Math. Surveys no. 9, Amer. Math. Soc. Providence, R. I. MR 158203
40.
A. Sard and S. Weintraub [1971], A book of splines, Wiley, New York. MR 283961
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).
42.
I. Schoenberg [1973], Cardinal spline interpolation, CBMS 12, SIAM, Philadelphia. MR 420078
43.
M. Schultz [1973], Spline analysis, Prentice-Hall, Englewood Cliffs, N. J. MR 362832
44.
G. Strang and G. Fix [1973], An analysis of the finite element method, Prentice-Hall, Englewood Cliffs, N. J. MR 443377
45.
V. Tihomirov [1969], Best methods of approximation and interpolation of differentiahle functions in the space C[-1, 1], Mat. Sb. 80, 290-304. MR 256043
46.
A. Timan [1963], Theory of approximation of functions of a real variable, McMillan, New York. MR 192238
47.
R. Varga [1962], Matrix iterative analysis, Prentice-Hall, Englewood Cliffs, N. J. MR 158502


Additional Information:

Reviewer(s):
Joseph W. Jerome

Review Information:
Journal: Bull. Amer. Math. Soc. 6 (1982), 238-247.
DOI: 10.1090/S0273-0979-1982-14996-5
PII: S 0273-0979(1982)14996-5


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google