Computation of transformed linear Chebyshev approximations

Abstract

A transformed linear approximation is a function of the form w(x) φ(L(A, x)), where L(A, ·) is an element of an n-dimensional linear space. Best Chebyshev approximations are characterized when φ is an order function. Computation of a best approximation on an n + 1 point set is considered. A variant of Stiefel's exchange (ascent) method is proposed for computation of best approximations on finite sets. It is shown that Stiefel's exchange increases the deviation under favorable circumstances. Best approximations on infinite sets can be obtained by discretization. © 1978.