Partitioned Triangular Tridiagonalization
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Partitioned Triangular Tridiagonalization
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/IAA100300802" target="_blank" >IAA100300802: Theory of Krylov subspace methods and its relationship to other mathematical disciplines</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ACM Transactions on Mathematical Software
ISSN
0098-3500
e-ISSN
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Volume of the periodical
37
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
"38:1"-"38:16"
UT code for WoS article
000287849900001
EID of the result in the Scopus database
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