Approximations with rational polynomials
Authors:
Ladis D. Kovach and Ronald V. Larson
Journal:
Quart. Appl. Math. 25 (1968), 463-467
MSC:
Primary 65.20
DOI:
https://doi.org/10.1090/qam/226819
MathSciNet review:
226819
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Abstract: One of the cornerstones of mathematical analysis is the use of Maclaurin’s series for the representation of transcendental functions. The advent of the electronic computer, however, has caused attention to be focussed on truncated, series. A number of techniques have been developed with the object of finding the “best” approximation to a transcendental function. The present paper describes a new technique by means of which such functions can be represented with a minimum number of terms.
- Cornelius Lanczos, Applied analysis, Prentice Hall, Inc., Englewood Cliffs, N. J., 1956. MR 0084175
- Ladis D. Kovach, A unique approach to the approximation of trigonometric functions, Amer. Math. Monthly 68 (1961), 839–846. MR 134454, DOI https://doi.org/10.2307/2311680
- F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956. MR 0075670
- Cecil Hastings Jr., Approximations for digital computers, Princeton University Press, Princeton, N. J., 1955. Assisted by Jeanne T. Hayward and James P. Wong, Jr. MR 0068915
C. W. Clenshaw, Chebyshev series for mathematical functions, Math. Tables No. 5 N.P.L., London HMSO, 1962
C. Lanczos, Applied analysis, Prentice-Hall, Englewood Cliffs, N. J., 1956
L. D. Kovach and W. Comley, A unique approach to the approximation of trigonometric functions, Amer. Math. Monthly (68) 9, 839–846 (1961)
F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill, New York, 1956
C. Hastings, Jr., Approximations for digital computers, Princeton University Press, Princeton, N. J., 1955
C. W. Clenshaw, Chebyshev series for mathematical functions, Math. Tables No. 5 N.P.L., London HMSO, 1962
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Article copyright:
© Copyright 1968
American Mathematical Society