Naslov
New fast and accurate Jacobi SVD algorithm. I

Autori
Drmač, Zlatko ; Veselić, Krešimir

Izvornik
SIAM journal on matrix analysis and applications (0895-4798) 29 (2008), 4; 1322-1342

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Jacobi method; singular value decomposition; eigenvalues

Sažetak
This paper is the result of concerted efforts to break the barrier between numerical accuracy and run time efficiency in computing the fundamental decomposition of numerical linear algebra -- the singular value decomposition (SVD) of general dense matrices. It is an unfortunate fact that the numerically most accurate one--sided Jacobi SVD algorithm is several times slower than generally less accurate bidiagonalization based methods such as the QR or the divide and conquer algorithm. Our quest for a highly accurate and efficient SVD algorithm has led us to a new, superior variant of the Jacobi algorithm. The new algorithm has inherited all good high accuracy properties of the Jacobi algorithm, and it can outperform the QR algorithm.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
Ovaj rad je rezultat istraživanja započetih i velikim dijelom završenih na prethodnom projektu 0037120. Drugi dio rada je objavljen u istom časopisu. Kako se radilo o dugoročnom opsežnom istraživanju, oba rada su preliminarno objavljena kako LAPACK Working notes pod brojevima 169 i 170 (http://www.netlib.org/lapack/lawns/downloads/). Proces recenziranja je trajao dugo i radovi su nakon finalne revizije konačno tiskani u siječnju 2008. Ovaj rad je nagradjen prestižnom strukovnom nagradom SIAG/Linear Algebra Prize, za najbolji rad u području primijenjene linearne algebre u trogodišnjem periodu, http://www.siam.org/prizes/sponsored/siagla.php O nagradjenim radovima se može pročitati u SIAM News na URL adresi http://www.siam.org/pdf/news/1696.pdf

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