Constrained minimax approximation and optimal preconditioners for Toeplitz matrices (Q1315215)

The authors consider an application of constrained minimax approximation to find preconditioners for symmetric Toeplitz systems generated by a \(2 \pi\)-periodic function based on polynomial approximations. A spectral analysis of the preconditioned system in terms of the minimax norm of the approximation problem is presented. The Remez algorithm is modified to handle the constraints. The theoretical results are illustrated by means of numerical examples.