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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.
Date30 October 1998
CreatorsBenhammouda, B.
PublisherTechnische Universität Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
Detected LanguageEnglish
Typedoc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text

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