T.F. CHAN AND P.C. HANSEN, Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations. SIAM J. Sci. Stat. Comput. 11 (1990), pp. 519-530. Home/Search Document Not in Database Summary Related Articles Check |
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The QLP Approximation to the Singular Value Decomposition - Stewart (1997) (Correct)
....zero, however, there is an increasingly great gap between the next to last and last singular values, while the ratio of the corresponding R values remains near one. This example has inspired researchers to look for other pivoting strategies under the rubric of rank revealing QR decompositions [2, 3, 4, 5, 7, 8]. There are, however, certain limitations to any pivoted QR decomposition. For example, the first R value is the norm of the first column of A Pi R . We hope this number will approximate oe 1 , which, however, is the spectral norm of the entire matrix A. Thus r 11 will in general underestimate oe ....
T. F. Chan and P. C. Hansen. Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations. SIAM Journal on Scientific and Statistical Computing, 11:519--530, 1990.
On Jacobi-Like Algorithms for Computing the Ordinary.. - Poul M. Rands Jensen (1991) (2 citations) (Correct)
....the singular values and a set of linear independent vectors which span an approximation to the null space. Since this is sufficient for solving a number of problems and since the RRQR is only slightly more computational complex than a QR decomposition, the RRQR factorization is often feasible, cf. [5, 6]. Given a matrix, A, with rank, r, its RRQR factorization is given as: A Pi = QR = Q R 11 R 12 0 R 22 ; 3.4) where Pi is a permutation matrix, Q is unitary, R 11 2 R r Thetar with condition number equal to oe 1 oe r and kR 12 k is of order oe r 1 . By initially computing any QR ....
....to oe 1 oe r and kR 12 k is of order oe r 1 . By initially computing any QR decomposition of A and next form Pi iteratively by building up R 22 one row at a time, estimates of the smallest singular values and associated right singular vectors are obtained. Further details can be found in e.g. [4, 5, 6]. 3.2 Jacobi like Algorithms The Jacobi algorithm composes a method for computing the eigenvalue decomposition of a real, square and symmetric matrix, A 2 R N ThetaN , and was original proposed by Jacobi in 1846 [19] Iteratively applying planar rotations, in this case known as Jacobi ....
T. F. Chan and P. C. Hansen. Computing Truncated Singular Value Decomposition Least Square Solutions by Rank Revealing QR--Factorization. SIAM Journal on Scientific and Statistical Computing, 11(3), 1990.
On an Inexpensive Triangular Approximation to the Singular Value.. - Stewart (1997) (Correct)
....from zero, however, there is an increasingly great gap between the next to last and last singular values, while the ratio of the corresponding R values remains near one. This example has inspired researchers to look for other pivoting strategies under the rubric of rank revealing QR decompositions [2, 3, 4, 5, 7, 8]. There are, however, certain limitations to any pivoted QR decomposition. For example, the first R value is the norm of the first column of A Pi R . We hope this number will approximate oe 1 , which, however, is the spectral norm of the entire matrix A. Thus r 11 will in general underestimate oe ....
T. F. Chan and P. C. Hansen. Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations. SIAM Journal on Scientific and Statistical Computing, 11:519--530, 1990.
Low-Rank Orthogonal Decompositions for Information Retrieval.. - Berry, Fierro (1996) (16 citations) (Correct)
.... can be a drawback for recursive procedures which require simple matrix updates (e.g. appending or deleting a row or column) Alternatively, rank revealing QR (RRQR) algorithms such as those by Foster [15] Chan [6] and modifications [4] can be used to obtain subspace information from matrices [7], 8] RRQR decompositions, however, yield subspaces whose accuracies depend on the gap in the singular values [13] in the sense that a large gap is required to produce good approximations to the singular subspaces. In LSI applications there is a small gap between the smallest singular value that ....
T. F. Chan and P. C. Hansen. Computing Truncated Singular Value Decomposition Least Squares Solutions by Rank Revealing QR Factorizations. SIAM Journal on Scientific and Statistical Computing, 11:519--530, 1990.
An Efficient Total Least Squares Algorithm Based on a.. - Van Huffel, Zha (1993) (Correct)
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T.F. CHAN AND P.C. HANSEN, Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations. SIAM J. Sci. Stat. Comput. 11 (1990), pp. 519-530.
A Schur Method for Low-Rank Matrix Approximation - van der Veen (1996) (2 citations) (Correct)
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T.F. CHAN AND P.C. HANSEN, Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations, SIAM J. Sci. Stat. Comput., 11 (1990), pp. 519--530.
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