Rank revealing QR factorizations

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An algorithm is presented for computing a column permutation Π and a O ̧R factorization AΠ = QR of an m by n (m≥n) matrix A such that a possible rank deficiency of A will be revealed in the triangular factor R having a small lower right block. For matrices of low rank deficiency, the algorithm is guaranteed to reveal the rank of A, and the cost is only slightly more than the cost of one regular O ̧R factorization. A posteriori upper and lower bounds on the singular values of A are derived and can be used to infer the numerical rank of A. © 1987.
Original languageEnglish
Pages (from-to)67-82
Number of pages16
JournalLinear Algebra and Its Applications
Issue numberC
StatePublished - 1987
Externally publishedYes


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