Residual and Backward Error Bounds in Minimum Residual Krylov Subspace Methods

0404084 - UIVT-O 20020010 RIV US eng J - Článek v odborném periodiku
Paige, C. C. - Strakoš, Zdeněk
Residual and Backward Error Bounds in Minimum Residual Krylov Subspace Methods.
SIAM Journal on Scientific Computing. Roč. 23, č. 6 (2002), s. 1899-1924. ISSN 1064-8275. E-ISSN 1095-7197
Grant CEP: GA AV ČR IAA1030103
Výzkumný záměr: AV0Z1030915
Klíčová slova: linear equations * eigenproblem * large sparse matrices * iterative solutions * Krylov subspace methods * Arnoldi method * GMRES * modified Gram-Schmidt * least squares * total least squares * singular values
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.291, rok: 2002

In this paper theoretical results of [C. Paige and Z. Strakoš, Bounds for the least squares distance using scaled total least squares, Numer. Math., to appear] are extended to the GMRES context. The bounds that are developed are important in theory, but they also have fundamental practical implications for the finite precision behavior of the modified Gram-Schmidt implementation of GMRES, and perhaps for other minimum norm methods.
Trvalý link: http://hdl.handle.net/11104/0124355