A Survey of Methods of Computing Minimax and Near-Minimax Polynomial Approximations for Functions of a Single Independent Variable

Authors:
W. Fraser
Affiliations:
Institute of Computer Science, University of Toronto, Canada
Venue:
Journal of the ACM (JACM)
Year:
1965

Citing 1
Cited 4

Conversion of a power to a series of Chebyshev polynomials

Communications of the ACM

Efficiency of a Procedure for Near-Minimax Approximation

Journal of the ACM (JACM)
Algorithm 414: Chebyshev approximation of continuous functions by a Chebyshev system of functions

Communications of the ACM
Chebyshev series expansion of inverse polynomials

Journal of Computational and Applied Mathematics
A Linear Time Algorithm for Near Minimax Continuous Piecewise Linear Representations of Discrete Data

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.03

Visualization

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.