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... Ausführliche Beschreibung

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veröffentlicht: Universitätsbibliothek Chemnitz, 1998
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041 |a eng 
037 |n urn:nbn:de:bsz:ch1-199801313 
100 |a Benhammouda, B. 
245 |a Rank-revealing top-down ULV factorizations 
260 |b Universitätsbibliothek Chemnitz  |c 1998  |9 (issued 1998-10-30) 
520 3 |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. 
500 |a preprint 
856 4 1 |u https://nbn-resolving.org/urn:nbn:de:bsz:ch1-199801313  |z Online-Zugriff 
650 4 |a MSC 65F15 
082 0 |a 510 
980 |a urn:nbn:de:bsz:ch1-199801313  |b 22  |c sid-22-col-qucosa 
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