The Role Eigenvalues Play in Forming GMRES Residual Norms with Non-Normal Matrices

0430466 - ÚI 2015 RIV NL eng J - Journal Article
Meurant, G. - Duintjer Tebbens, Jurjen
The Role Eigenvalues Play in Forming GMRES Residual Norms with Non-Normal Matrices.
Numerical Algorithms. Roč. 68, č. 1 (2015), s. 143-165. ISSN 1017-1398. E-ISSN 1572-9265
R&D Projects: GA ČR GA13-06684S
Institutional support: RVO:67985807
Keywords : GMRES convergence * non-normal matrix * eigenvalues * residual norms
Subject RIV: BA - General Mathematics
Impact factor: 1.366, year: 2015

In this paper we give explicit expressions for the norms of the residual vectors generated by the GMRES algorithm applied to a non-normal matrix. They involve the right-hand side of the linear system, the eigenvalues, the eigenvectors and, in the non-diagonalizable case, the principal vectors. They give a complete description of how eigenvalues contribute in forming residual norms and offer insight in what quantities can prevent GMRES from being governed by eigenvalues.
Permanent Link: http://hdl.handle.net/11104/0235396