Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4645244 | Applied Numerical Mathematics | 2014 | 8 Pages |
Abstract
In this paper we give necessary and sufficient conditions for the complete or partial stagnation of the GMRES iterative method for solving real linear systems. Our results rely on a paper by Arioli, Pták and Strakoš (1998), characterizing the matrices having a prescribed convergence curve for the residual norms. We show that we have complete stagnation if and only if the matrix A is orthonormally similar to an upper or lower Hessenberg matrix having a particular first row or column or a particular last row or column. Partial stagnation is characterized by a particular pattern of the matrix Q in the QR factorization of the upper Hessenberg matrix generated by the Arnoldi process.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Gérard Meurant,