Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
The dynamics of matrix coupling with an application to krylov methods
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
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Krylov methods are, since their introduction in the 1980s, the most heavily used methods to solve the two problems Ax = b and Ax = 驴x, x 驴= 0 where the matrix A is very large.However, the understanding of their numerical behaviour is far from satisfactory. We propose a radically new viewpoint for this longstanding enigma, which shows mathematically that the Krylov-type method works best when it is most ill-conditioned.