On the field of values and pseudospectra of the inverse of a large matrix
Michiel E. Hochstenbach, DA Singer, PF Zachlin · 2007
Abstract. We consider the approximation of the field of values of the inverse of a large sparse matrix, without explicitly computing the inverse or using its action (i.e., accurately solving a linear system with this matrix). We review results by Manteuffel and Starke and give an alternative that may be better approximations in practice. We give connections with the harmonic Rayleigh–Ritz approach and also study the approximation of the pseudospectra of a matrix inverse. We give several applications of the studied concepts as well as numerical examples.