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Partitioned Triangular Tridiagonalization
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SYSNO ASEP 0310891 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Partitioned Triangular Tridiagonalization Tvůrce(i) Rozložník, Miroslav (UIVT-O) SAI, RID, ORCID
Shklarski, G. (IL)
Toledo, S. (IL)Zdroj.dok. ACM Transactions on Mathematical Software. - : Association for Computing Machinery - ISSN 0098-3500
Roč. 37, č. 4 (2011), 38:1-38:16Poč.str. 16 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova algorithms ; performance ; symmetric indefinite matrices ; tridiagonalization ; Aasen's tridiagonalization ; Parlett-Reid tridiagonalization ; partitioned factorizations ; recursive factorizations Vědní obor RIV BA - Obecná matematika CEP IAA100300802 GA AV ČR - Akademie věd CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000287849900001 EID SCOPUS 79952496435 DOI 10.1145/1916461.1916462 Anotace We present a partitioned algorithm for reducing a symmetric matrix to a tridiagonal form, with partial pivoting. That is, the algorithm computes a factorization PAPT = LTLT, where, P is a permutation matrix, L is lower triangular with a unit diagonal and entries’ magnitudes bounded by 1, and T is symmetric and tridiagonal. The algorithm is based on the basic (nonpartitioned) methods of Parlett and Reid and of Aasen. We show that our factorization algorithm is componentwise backward stable (provided that the growth factor is not too large), with a similar behavior to that of Aasen’s basic algorithm. Our implementation also computes the QR factorization of T and solves linear systems of equations using the computed factorization. The partitioning allows our algorithm to exploit modern computer architectures (in particular, cache memories and high-performance blas libraries). Experimental results demonstrate that our algorithms achieve approximately the same level of performance as the partitioned Bunch-Kaufman factor and solve routines in lapack. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2012
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