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Convergence of GMRES for Tridiagonal Toeplitz Matrices
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SYSNO ASEP 0103272 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Convergence of GMRES for Tridiagonal Toeplitz Matrices Překlad názvu Konvergence metody GMRES pro třídiagonální Toeplitzovské matice Tvůrce(i) Liesen, J. (DE)
Strakoš, Zdeněk (UIVT-O) SAI, RID, ORCIDZdroj.dok. SIAM Journal on Matrix Analysis and Applications. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0895-4798
Roč. 26, č. 1 (2004), s. 233-251Poč.str. 19 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova Krylov subspace methods ; GMRES ; minimal residual methods ; convergence analysis ; Jordan blocks ; Toeplitz matrices Vědní obor RIV BA - Obecná matematika CEP GA201/02/0595 GA ČR - Grantová agentura ČR CEZ AV0Z1030915 - UIVT-O UT WOS 000225642900011 EID SCOPUS 14544308440 DOI https://doi.org/10.1137/S0895479803424967 Anotace We analyze the residuals of GMRES, when the method is applied to tridiagonal Toeplitz matrices. We first derive formulas for the residuals as well as their norms when GMRES is applied to scaled Jordan blocks. This problem has been studied previously by Ipsen and Eiermann and Ernst, but we formulate and prove our results in a different way. Intuitively, when a scaled Jordan block is extended to a tridiagonal Toeplitz matrix by a superdiagonal of small modulus (compared to the modulus of the subdiagonal), the GMRES residual norms for both matrices and the same initial residual should be close to each other. We confirm and quantify this intuitive statement. We also demonstrate principal difficulties of any GMRES convergence analysis which is based on eigenvector expansion of the initial residual when the eigenvector matrix is ill-conditioned. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2005
Počet záznamů: 1