A Survey of Methods of Computing Minimax and Near-Minimax Polynomial Approximations for Functions of a Single Independent Variable
- 1 July 1965
- journal article
- Published by Association for Computing Machinery (ACM) in Journal of the ACM
- Vol. 12 (3) , 295-314
- https://doi.org/10.1145/321281.321282
Abstract
Methods are described for the derivation of minimax and near-minimax polynomial approximations. For minimax approximations techniques are considered for both analytically defined functions and functions defined by a table of values. For near-minimax approximations methods of determining the coefficients of the Fourier-Chebyshev expansion are first described. These consist of the rearrangement of the coefficients of a power polynomial, and also direct determination of the coefficients from the integral which defines them, or the differential equation which defines the function. Finally there is given a convenient modification of an interpolation scheme which finds coefficients of a near-minimax approximation without requiring numerical integration or the numerical solution of a system of equations.Keywords
This publication has 3 references indexed in Scilit:
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- On the numerical determination of the best approximations in the Chebyshev senseNumerische Mathematik, 1960
- The numerical solution of linear differential equations in Chebyshev seriesMathematical Proceedings of the Cambridge Philosophical Society, 1957