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 yield better approximations in practice. We give connections with the harmonic Rayleigh-Ritz approach. Several properties and applications of the studied concepts as well as numerical examples are provided.
|Title of host publication||The Natália Bebiano anniversary volume|
|Editors||C. Fonseca, S. Furtado, A. Kovacec, C.-K. Li|
|Place of Publication||Coimbra|
|Publisher||University of Coimbra|
|Publication status||Published - 2013|
|Name||Textos de Matemática|