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: 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]**M. Abramowitz & I. A. Stegun,*Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables*, Nat. Bur. Standards, Appl. Math. Series No. 55, U. S. Government Printing Office, Washington, D. C., 1964. MR**0167642 (29:4914)****[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 et al.,*Handbook for Computing Elementary Functions*, Pergamon Press, New York, 1965. MR**0183102 (32:584)****[5]**R. Savage & E. 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*, Nat. Bur. Standards, Appl. Math. Series No. 39, U. S. Government Printing Office, Washington, D. C., 1954, pp. 105-108. MR**0068303 (16:861d)****[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