Abstract
Krylov methods are, since their introduction in the 1980s, the most heavily used methods to solve the two problems Ax = b and Ax = λx, x ≠ 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.
CERFACS Technical Report TR/PA/00/40
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Chaitin-Chatelin, F., Traviesas, E., Plantié, L. (2001). Understanding Krylov Methods in Finite Precision. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_23
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DOI: https://doi.org/10.1007/3-540-45262-1_23
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