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On GMRES for singular EP and GP systems
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SYSNO ASEP 0490058 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název On GMRES for singular EP and GP systems Tvůrce(i) Morikuni, K. (JP)
Rozložník, Miroslav (MU-W) RID, SAI, ORCIDZdroj.dok. SIAM Journal on Matrix Analysis and Applications. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0895-4798
Roč. 39, č. 2 (2018), s. 1033-1048Poč.str. 16 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova GMRES method ; singular linear systems ; least squares problems ; group inverse Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics Institucionální podpora MU-W - RVO:67985840 UT WOS 000436971900020 EID SCOPUS 85049744175 DOI 10.1137/17M1128216 Anotace In this contribution, we study the numerical behavior of the generalized minimal residual (GMRES) method for solving singular linear systems. It is known that GMRES determines a least squares solution without breakdown if the coefficient matrix is range-symmetric (EP) or if its range and nullspace are disjoint (GP) and the system is consistent. We show that the accuracy of GMRES iterates may deteriorate in practice due to three distinct factors: (i) the inconsistency of the linear system, (ii) the distance of the initial residual to the nullspace of the coefficient matrix, and (iii) the extremal principal angles between the ranges of the coefficient matrix and its transpose. These factors lead to poor conditioning of the extended Hessenberg matrix in the Arnoldi decomposition and affect the accuracy of the computed least squares solution. We also compare GMRES with the range restricted GMRES method. Numerical experiments show typical behaviors of GMRES for small problems with EP and GP matrices. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2019
Počet záznamů: 1