Partitioned Triangular Tridiagonalization

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F11%3A00310891" target="_blank" >RIV/67985807:_____/11:00310891 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1145/1916461.1916462" target="_blank" >http://dx.doi.org/10.1145/1916461.1916462</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/1916461.1916462" target="_blank" >10.1145/1916461.1916462</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Partitioned Triangular Tridiagonalization

Popis výsledku v původním jazyce

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 andentries? 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 thatthe 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 allowsour 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 pa

Název v anglickém jazyce

Partitioned Triangular Tridiagonalization

Popis výsledku anglicky

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 andentries? 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 thatthe 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 allowsour 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 pa

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/IAA100300802" target="_blank" >IAA100300802: Teorie metod Krylovových podprostorů a její vztah k jiným oblastem matematiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ACM Transactions on Mathematical Software

ISSN

0098-3500

e-ISSN

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Svazek periodika

37

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

"38:1"-"38:16"

Kód UT WoS článku

000287849900001

EID výsledku v databázi Scopus

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