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Rank Revealing QR-factorizations

Tony F. Chan

出版	Yale University, Department of Computer Science, 1985
URL	http://books.google.com.hk/books?id=36fQygAACAAJ&hl=&source=gbs_api

註釋

An algorithm is presented for computing a column permutation Pi and a QR-factorization (A)(Pi) = QR of an m by n (m> or = 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 low rank deficient matrices, the algorithm is guaranteed to reveal the rank of A and the cost is only slightly more than the cost of one regular QR-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. Keywords: QR-Factorization; Rank deficient matrices; Least squares computation; Subset selection; Rank; Singular values.