A general method of approximation. I

Authors:
Staffan Wrigge and Arne Fransén

Journal:
Math. Comp. **38** (1982), 567-588

MSC:
Primary 41A50; Secondary 15A57, 65D15

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645672-9

MathSciNet review:
645672

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study two families of functions, viz. *F* and *H*, and show how to approximate the functions considered in the interval [0,1 ]. The functions are assumed to be real when the argument is real.

We define

The associated matrices are analyzed using the theory of orthogonal polynomials, especially the Jacobi polynomials . We apply the general theory to the basic trigonometric functions and .

**[1]**Milton Abramowitz and Irene A. Stegun,*Handbook of mathematical functions with formulas, graphs, and mathematical tables*, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR**0167642****[2]**F. Ayres, Jr.,*Theory and Problems of Matrices*, Schaum Publishing Company, 1962.**[3]**H. Cramér,*Mathematical Methods of Statistics*, 10th ed., Princeton Univ. Press, Princeton, N. J., 1963.**[4]**L. A. Lyusternik, O. A. Chervonenkis, and A. R. Yanpol′skii,*Handbook for computing elementary functions*, Translated from the Russian by G. J. Tee. Translation edited by K. L. S tewart, Pergamon Press, Oxford-Edinburg-New York, 1965. MR**0183102****[5]**Richard Savage and Eugene Lukacs,*Tables of inverses of finite segments of the Hilbert matrix*, Contributions to the solution of systems of linear equations and the determination of eigenvalues, National Bureau of Standards Applied Mathematics Series No. 39, U. S. Government Printing Office, Washington, D. C., 1954, pp. 105–108. MR**0068303****[6]**S. Wrigge, A. Fransén & G. Borenius,*Rapid Calculation of*, FOA Rapport, C 10150-M8, National Defence Research Institute, S 104 50 Stockholm 80, Sweden, 1980.**[7]**S. Wrigge, A. Fransén & G. Borenius,*A General Method of Approximation, Particularly in*, FOA Rapport C 10158-M8, National Defence Research Institute, S 104 50 Stockholm 80, Sweden, 1980.**[8]**S. Wrigge,*A General Method of Approximation Associated with Bernstein Polynomials*, FOA Rapport, C 10170-M8, National Defence Research Institute, S 104 50 Stockholm 80, Sweden, 1980.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645672-9

Keywords:
Approximation theory,
inverse matrices,
Jacobi polynomials

Article copyright:
© Copyright 1982
American Mathematical Society