Convergence of Best Rational Tchebycheff Approximations

by Barry W. Boehm

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Some bounds are established for the maximum deviation of an approximating rational function from a given function, in terms of continuity properties of the given function and the degrees of the polynomials comprising the rational function. Estimates of the rapidity of convergence of best rational Tchebycheff approximations are given, along with examples of nonconvergence phenomena and of functions to which convergence is arbitrarily slow. 26 pp.

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