Extremal Polynomials with Application to Richardson Iteration for Indefinite Linear Systems
Carl de Boor, John R. Rice · SIAM Journal on Scientific and Statistical Computing · 1982
The application of Richardson iteration to a symmetric, but indefinite linear system requires certain parameters which can be determined from the zeros in the error of a certain best polynomial approximant on some set S known to contain the spectrum of the coefficient matrix. It is pointed out that this error can also be obtained as a multiple of the extremal polynomial for the linear functional $p \mapsto p(0)$, and this leads to an efficient Remes type algorithm for its determination. A program incorporating this algorithm for the case that S consists of two or more intervals bracketing zero is available.