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Rank-revealing top-down ULV factorizations

Personen und Körperschaften: Benhammouda, B.
Titel: Rank-revealing top-down ULV factorizations
Format: E-Artikel
veröffentlicht:
Chemnitz Technische Universität Chemnitz
Online-Ausg.. 1998
Schlagwörter:
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245 |a Rank-revealing top-down ULV factorizations 
264 |a Chemnitz  |b Technische Universität Chemnitz 
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520 |a Rank-revealing ULV and URV factorizations are useful tools to determine the rank and to compute bases for null-spaces of a matrix. However, in the practical ULV (resp. URV ) factorization each left (resp. right) null vector is recomputed from its corresponding right (resp. left) null vector via triangular solves. Triangular solves are required at initial factorization, refinement and updating. As a result, algorithms based on these factorizations may be expensive, especially on parallel computers where triangular solves are expensive. In this paper we propose an alternative approach. Our new rank-revealing ULV factorization, which we call ¨top-down¨ ULV factorization ( TDULV -factorization) is based on right null vectors of lower triangular matrices and therefore no triangular solves are required. Right null vectors are easy to estimate accurately using condition estimators such as incremental condition estimator (ICE). The TDULV factorization is shown to be equivalent to the URV factorization with the advantage of circumventing triangular solves. 
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contents Rank-revealing ULV and URV factorizations are useful tools to determine the rank and to compute bases for null-spaces of a matrix. However, in the practical ULV (resp. URV ) factorization each left (resp. right) null vector is recomputed from its corresponding right (resp. left) null vector via triangular solves. Triangular solves are required at initial factorization, refinement and updating. As a result, algorithms based on these factorizations may be expensive, especially on parallel computers where triangular solves are expensive. In this paper we propose an alternative approach. Our new rank-revealing ULV factorization, which we call ¨top-down¨ ULV factorization ( TDULV -factorization) is based on right null vectors of lower triangular matrices and therefore no triangular solves are required. Right null vectors are easy to estimate accurately using condition estimators such as incremental condition estimator (ICE). The TDULV factorization is shown to be equivalent to the URV factorization with the advantage of circumventing triangular solves.
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spelling Benhammouda, B., Rank-revealing top-down ULV factorizations, Chemnitz Technische Universität Chemnitz, Online-Ausg. 1998 Online-Ressource (Text) Universitätsbibliothek Chemnitz, Rank-revealing ULV and URV factorizations are useful tools to determine the rank and to compute bases for null-spaces of a matrix. However, in the practical ULV (resp. URV ) factorization each left (resp. right) null vector is recomputed from its corresponding right (resp. left) null vector via triangular solves. Triangular solves are required at initial factorization, refinement and updating. As a result, algorithms based on these factorizations may be expensive, especially on parallel computers where triangular solves are expensive. In this paper we propose an alternative approach. Our new rank-revealing ULV factorization, which we call ¨top-down¨ ULV factorization ( TDULV -factorization) is based on right null vectors of lower triangular matrices and therefore no triangular solves are required. Right null vectors are easy to estimate accurately using condition estimators such as incremental condition estimator (ICE). The TDULV factorization is shown to be equivalent to the URV factorization with the advantage of circumventing triangular solves., Msc 65F15, text/html https://nbn-resolving.org/urn:nbn:de:bsz:ch1-199801313 Online-Zugriff
spellingShingle Benhammouda, B., Rank-revealing top-down ULV factorizations, Rank-revealing ULV and URV factorizations are useful tools to determine the rank and to compute bases for null-spaces of a matrix. However, in the practical ULV (resp. URV ) factorization each left (resp. right) null vector is recomputed from its corresponding right (resp. left) null vector via triangular solves. Triangular solves are required at initial factorization, refinement and updating. As a result, algorithms based on these factorizations may be expensive, especially on parallel computers where triangular solves are expensive. In this paper we propose an alternative approach. Our new rank-revealing ULV factorization, which we call ¨top-down¨ ULV factorization ( TDULV -factorization) is based on right null vectors of lower triangular matrices and therefore no triangular solves are required. Right null vectors are easy to estimate accurately using condition estimators such as incremental condition estimator (ICE). The TDULV factorization is shown to be equivalent to the URV factorization with the advantage of circumventing triangular solves., Msc 65F15
title Rank-revealing top-down ULV factorizations
title_auth Rank-revealing top-down ULV factorizations
title_full Rank-revealing top-down ULV factorizations
title_fullStr Rank-revealing top-down ULV factorizations
title_full_unstemmed Rank-revealing top-down ULV factorizations
title_short Rank-revealing top-down ULV factorizations
title_sort rank-revealing top-down ulv factorizations
title_unstemmed Rank-revealing top-down ULV factorizations
topic Msc 65F15
topic_facet Msc 65F15
url https://nbn-resolving.org/urn:nbn:de:bsz:ch1-199801313
urn urn:nbn:de:bsz:ch1-199801313
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