Efficient algorithms for computing a strong rank-revealing QR factorization

Journal Article · Mon Jul 01 00:00:00 EDT 1996 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/0917055· OSTI ID:276532

Gu, M ^[1]; Eisenstat, S C ^[2]

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1. Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
2. Yale Univ., New Haven, CT (United States). Dept. of Computer Science

Given an m x n matrix M with m {ge} n, it is shown that there exists a permutation {Pi} and an integer k such that the QR factorization given by equation (1) reveals the numerical rank of M: the k x k upper-triangular matrix A{sub k} is well conditioned, norm of (C{sub k}){sub 2} is small, and B{sub k} is linearly dependent on A{sub k} with coefficients bounded by a low-degree polynomial in n. Existing rank-revealing QR (RRQR) algorithms are related to such factorizations and two algorithms are presented for computing them. The new algorithms are nearly as efficient as QR with column pivoting for most problems and take O(mn{sup 2}) floating-point operations in the worst case.

• Sponsoring Organization: USDOE
• OSTI ID: 276532
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 4 Vol. 17; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
FACTORIZATION
MATRICES
MATRIX ELEMENTS
POLYNOMIALS
USES