On the application of orthogonal polynomials to the iterative solution of linear systems of equations with indefinite or non-Hermitian matrices (Q1090062)

For large linear systems of equations \(Ax=b\) where the eigenvalues of A lie in one or more several known simple connected regions \(S_ j\), \(j=1(1)\ell\), in the complex plane, relaxation methods using polynomials \(\{p_ n(z)\}^{\infty}_{n=0}\) orthogonal on the boundary of \(\cup^{\ell}_{j=1}S_ j\) are presented. The rate of convergence is shown to be asymptotically optimal. Numerical examples are given.