Author： Pan C-T.
Publisher： Springer Publishing Company
ISSN： 0006-3835
Source： Bit Numerical Mathematics, Vol.39, Iss.4, 1999-01, pp. : 740-756
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Abstract
We introduce a pair of dual concepts: pivoted blocks and reverse pivoted blocks. These blocks are the outcome of a special column pivoting strategy in QR</i> factorization. Our main result is that under such a column pivoting strategy, the QR</i> factorization of a given matrix can give tight estimates of any two a priori-chosen consecutive singular values of that matrix. In particular, a rank-revealing QR</i> factorization is guaranteed when the two chosen consecutive singular values straddle a gap in the singular value spectrum that gives rise to the rank degeneracy of the given matrix. The pivoting strategy, called cyclic pivoting, can be viewed as a generalization of Golub's column pivoting and Stewart's reverse column pivoting. Numerical experiments confirm the tight estimates that our theory asserts.
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