Least Squares Residuals and Minimal Residual Methods

0404002 - UIVT-O 20010018 RIV US eng J - Journal Article
Liesen, J. - Rozložník, Miroslav - Strakoš, Zdeněk
Least Squares Residuals and Minimal Residual Methods.
SIAM Journal on Scientific Computing. Roč. 23, č. 5 (2002), s. 1503-1525. ISSN 1064-8275. E-ISSN 1095-7197
R&D Projects: GA AV ČR IAA1030103
Institutional research plan: AV0Z1030915
Keywords : linear systems * least squares problems * Krylov subspace methods * minimal residual methods * GMRES * convergence * rounding errors
Subject RIV: BA - General Mathematics
Impact factor: 1.291, year: 2002

We study Krylov subspace methods for solving unsymmetric linear algebraic systems that minimize the norm of the residual at each step (minimal residual (MR) methods). MR methods are often formulated in terms of a sequence of least squares (LS) problems of increasing dimension. We present several basic identities and bounds for the LS residual. These results are interesting in the general context of solving LS problems. When applied to MR methods, they show that the size of the MR residual is strongly...
Permanent Link: http://hdl.handle.net/11104/0124283