Once again on solving systems of linear equations whose coefficient matrices are low-rank perturbations of Hermitian matrices

Abstract

MINRES-N is a minimal residual algorithm, originally developed by the authors for solving systems of linear equations with normal coefficient matrices whose spectra lie on algebraic curves of low degree. In a previous publication, the authors showed that a variant of MINRES-N, called MINRES-N2, is applicable to nonnormal matrices A satisfying the condition $$rank (A - A^ * ) = 1$$ . This fact is extended to nonnormal matrices A such that $$rank (A - A^ * ) = k, k \geqslant 1$$ . Bibliography: 2 titles.