James Demmel, Ming Gu, Stanley Eisenstat, Ivan Slapnicar, Kresimir Veselic, Zlatko Drmac  Home/Search
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Abstract: We analyze when it is possible to compute the singular values and singular vectors of a matrix with high relative accuracy. This means that each computed singular value is guaranteed to have some correct digits, even if the singular values have widely varying magnitudes. This is in contrast to the absolute accuracy provided by conventional backward stable algorithms, which in general only guarantee correct digits in the singular values with large enough magnitudes. It is of interest to compute... (Update)
Context of citations to this paper: More
...the singular value decomposition (SVD) to return an inaccurate computed smallest singular value. However, SVD methods developed in [8], 17] do not suffer from this difficulty as they are insensitive to the column scaling. The formula (2.7) requires computation of the SVD...
...of accurate floating point computation, in particular for matrix computations. A very short bibliography would include [10, 7, 8, 14, 12, 1, 9, 11, 2]. We consider the evaluation of multivariate rational functions r(x) of floating point numbers, and matrix computations on...
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10: The John Hopkins University Press (context) - Golub, Van Loan - 1989
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BibTeX entry: (Update)
J. Demmel, M. Gu, S. Eisenstat, I. Slapnicar and K. Veselic, Computing the Singular Value Decomposition with High Relative Accuracy, submitted to Linear Algebra & Applications. http://citeseer.ist.psu.edu/article/demmel98computing.html More
@misc{ relative-computing,
author = "James Demmel and Ming Gu and Stanley Eisenstat and Ivan Slapnicar and Kresimir Veselic and Zlatko Drmac",
title = "Computing the Singular Value Decomposition with High Relative Accuracy",
url = "citeseer.ist.psu.edu/article/demmel98computing.html" }
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441 The Symmetric Eigenvalue Problem (context) - Parlett - 1980
387 A set of Level 3 Basic Linear Algebra Subprograms (context) - Dongarra, Croz et al. - 1990
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78 Computing accurate eigensystems of scaled diagonally dominan.. - Barlow, Demmel - 1990
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35 Handbook for Automatic Computation (context) - Wilkinson, Reinsch - 1971
29 Accurate symmetric eigenreduction by a Jacobi method - Slapnicar - 1992
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27 Stable numerical algorithms for equilibrium systems - Vavasis - 1994
26 Relative perturbation techniques for singular value problems (context) - Eisenstat, Ipsen - 1995
25 Fernando's solution to Wilkinson's problem: An application o.. - Parlett, Dhillon - 1997
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17 Bounds on singular values revealed by QR factorization (context) - Pan, Tang - 1992
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15 Computing the Singular and the Generalized Singular Values (context) - Drmac - 1994
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3 Sturm-Liouville operator discretized (context) - Drmac, Veseli'c - 1996
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2 On bounds for scaled projections and pseudoinverses (context) - O'Leary - 1990
2 A note on the accuracy of symmetric eigenreduction algorithm.. - Veseli'c - 1996
2 Matrices and Invariants (context) - Turnbull, of - 1960
1 A generalized SVD analysis of some weighting methods for equ.. (context) - Van Loan - 1983
1 More accurate bidiagonal reduction for computing the singula.. - Barlow - 1998
1 Pinchings and norms of scaled triangular matrices - Li, Kahan et al. - 1998
1 A posteriori computation of the singular vectors in a precon.. (context) - Drmac - 1998
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1 Some new rank-revealing factorizations (context) - Gu - 1998
1 to appear in SIMAX; LAPACK Working Note (context) - Demmel, of - 1998
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