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Low‐rank revealing QR factorizations
Author(s) -
Chan Tony F.,
Hansen Per Christian
Publication year - 1994
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680010105
Subject(s) - rank (graph theory) , mathematics , qr decomposition , extension (predicate logic) , algorithm , selection (genetic algorithm) , connection (principal bundle) , subspace topology , combinatorics , eigenvalues and eigenvectors , computer science , artificial intelligence , mathematical analysis , physics , geometry , quantum mechanics , programming language
Rank revealing factorizations are used extensively in signal processing in connection with, for example, linear prediction and signal subspace algorithms. We present an algorithm for computing rank revealing QR factorizations of low‐rank matrices. The algorithm produces tight upper and lower bounds for all the largest singular values, thus making it particularly useful for treating rank deficient problems by means of subset selection, truncated QR, etc. The algorithm is similar in spirit to an algorithm suggested earlier by Chan for matrices with a small nullity, and it can also be considered as an extension of ordinary column pivoting.