Zur numerischen Stabilität des Newton-Verfahrens bei der nichtlinearen Tschebyscheff-Approximation

Abstract

When the nonlinear approximation problem is treated by using Newton's method, at each iteration step the solution of a linear approximation problem is required. If we are concerned with nonlinear Chebyshev approximation, the (linear) auxiliary problem is also non trivial. Thus for generating a more effective algorithm the latter problem is solved only on a finite point set. However, then we must not only choose reference points like in Remez-type algorithmus; the reference set has to be augmented in order to take care of numerical stability.