Rank revealing QR factorizations

T.F. Chan

doi:10.1016/0024-3795(87)90103-0

Rank revealing QR factorizations

T.F. Chan

Research output: Contribution to journal › Article › peer-review

381 Scopus citations

Abstract

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 language	English
Pages (from-to)	67-82
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	88-89
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(87)90103-0
State	Published - 1987
Externally published	Yes

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cited By 240

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title = "Rank revealing QR factorizations",

abstract = "An algorithm is presented for computing a column permutation Π and a O{\c }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{\c }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. {\textcopyright} 1987.",

author = "T.F. Chan",

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journal = "Linear Algebra and Its Applications",

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T1 - Rank revealing QR factorizations

AU - Chan, T.F.

N1 - cited By 240

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

U2 - 10.1016/0024-3795(87)90103-0

DO - 10.1016/0024-3795(87)90103-0

M3 - Article

SN - 0024-3795

VL - 88-89

SP - 67

EP - 82

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

Rank revealing QR factorizations

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