Počet záznamů: 1
Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems
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SYSNO ASEP 0438625 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems Tvůrce(i) Morikuni, Keiichi (UIVT-O)
Hayami, K. (JP)Zdroj.dok. SIAM Journal on Matrix Analysis and Applications. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0895-4798
Roč. 36, č. 1 (2015), s. 225-250Poč.str. 26 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova least squares problem ; iterative methods ; preconditioner ; inner-outer iteration ; GMRES method ; stationary iterative method ; rank-deficient problem Vědní obor RIV BA - Obecná matematika Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000352222700011 EID SCOPUS 84925297891 DOI 10.1137/130946009 Anotace We develop a general convergence theory for the generalized minimal residual method preconditioned by inner iterations for solving least squares problems. The inner iterations are performed by stationary iterative methods. We also present theoretical justifications for using specific inner iterations such as the Jacobi and SOR-type methods. The theory improves previous work [K. Morikuni and K. Hayami, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 1--22], particularly in the rank-deficient case. We also characterize the spectrum of the preconditioned coefficient matrix by the spectral radius of the iteration matrix for the inner iterations and give a convergence bound for the proposed methods. Finally, numerical experiments show that the proposed methods are more robust and efficient compared to previous methods for some rank-deficient problems. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2015
Počet záznamů: 1