Ricardo D. Fierro and Per Christian Hansen. Accuracy of TSVD Solutions Computed from Rank-Revealing Decompositions. Numerische Mathematik, 70:453--471, 1995. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Rank-Revealing "top-Down" Ulv Factorizations - Benhammouda (1997) (1 citation) (Correct)
....the numerical rank and bases for the null spaces. The ULV and the URV factorizations can be updated in O(n 2 ) flops, sequentially and in O(n) flops on an array of n processors [26, 27] Recent work related to the URV and ULV factorization both in theory and implementation may be found in [8, 9, 10, 11, 22, 23]. The rank revealing ULV and the URV algorithms are iterative and require estimates of the condition number of some triangular submatrices at every iteration step of initial factorization, refinement and updating. In the URV and the ULV factorizations small singular values and associated null ....
R. D. Fierro And P. C. Hansen, Accuracy of TSVD solutions computed from rank-revealing decompositions, Numer. Math. 70, (1995) 453471.
Signal Subspace Methods for Speech Enhancement - Hansen (1997) (10 citations) Self-citation (Hansen) (Correct)
No context found.
Ricardo D. Fierro and Per Christian Hansen. Accuracy of TSVD Solutions Computed from Rank-Revealing Decompositions. Numerische Mathematik, 70:453--471, 1995.
Ulv-Based Signal Subspace Methods For Speech Enhancement - Peter Hansen (1997) (1 citation) Self-citation (Hansen) (Correct)
....n (4) Thus, the signal and noise subspaces defined by the gap in the singular values can be estimated using the RRULVD, where the quality depends on kFX k 2 . An approximate LS estimate SALS of the signal matrix S can be computed by essentially substituting the RRULVD for the SVD based estimate [3], thus replacing one problem with a similar, nearby problem that can be solved more efficiently, i.e. SALS = XVX1V T X1 (5) The estimate converges to the true LS solution, if the following condition is satisfied ffl The off diagonal matrix FX is zero. Assume now that the estimator S of the ....
Ricardo D. Fierro and Per Christian Hansen. Accuracy of TSVD Solutions Computed from Rank-Revealing Decompositions. Numerische Mathematik, 70:453--471, 1995.
Noise Reduction Of Speech Signals Using The Rank-Revealing.. - Peter Hansen (1996) Self-citation (Hansen) (Correct)
....values. The tolerance is defined based on a detection threshold in the underlying signal processing problem. 4. 1 LS Estimate by RRULVD An approximate least squares estimate SALS of the signal matrix S can be computed by essentially substituting the ULV decomposition for the SVD based estimate [3], thus replacing one problem with a similar, nearby problem that can be solved more efficiently. Based on (5) and (11) a useful rank p matrix approximation to X is given by SALS = U1L1V T 1 = XV1V T 1 (14) where U1 and V1 approximate the numerical column space and row space as defined via ....
Ricardo D. Fierro and Per Christian Hansen. Accuracy of TSVD Solutions Computed from Rank-Revealing Decompositions. Numerische Mathematik, 70:453--471, 1995.
Low-Rank Orthogonal Decompositions for Information Retrieval.. - Berry, Fierro (1996) (16 citations) Self-citation (Fierro) (Correct)
.... 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 is retained and the largest singular value that is discarded, hence an RRQR decomposition is not appropriate for ....
....PAGE PROOFS paper Low Rank Orthogonal Decompositions for Information Retrieval 9 numerical rank. This is important for many ill conditioned least squares problems, for example, where one can then replace the problem with a nearby well conditioned one to compute a less sensitive solution, cf. [13]. Rank revealing algorithms applied to term by document matrices for LSI require special handling for the following reasons: ffl The numerical rank of the matrix is close to min(m; n) but only approximations of the k largest singular values and singular vectors are needed for LSI, where k ....
R. D. Fierro and P. C. Hansen. Accuracy of TSVD Solutions Computed From Rank Revealing Decompositions. Numerische Mathematik, 70:453--471, 1995.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC