On the asymptotic behavior of scaled singular value and $QR$ decompositions
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- by G. W. Stewart PDF
- Math. Comp. 43 (1984), 483-489 Request permission
Abstract:
Asymptotic expressions are derived for the singular value decompositon of a matrix some of whose columns approach zero. Expressions are also derived for the QR factorization of a matrix some of whose rows approach zero. The expressions give insight into the method of weights for approximating the solutions of constrained least squares problems.References
- Charles L. Lawson and Richard J. Hanson, Solving least squares problems, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. MR 0366019
- G. W. Stewart, Error and perturbation bounds for subspaces associated with certain eigenvalue problems, SIAM Rev. 15 (1973), 727–764. MR 348988, DOI 10.1137/1015095
- G. W. Stewart, Rank degeneracy, SIAM J. Sci. Statist. Comput. 5 (1984), no. 2, 403–413. MR 740857, DOI 10.1137/0905030
- Gilbert Strang, Linear algebra and its applications, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0384823
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp. 43 (1984), 483-489
- MSC: Primary 65F35; Secondary 15A23, 65D10
- DOI: https://doi.org/10.1090/S0025-5718-1984-0758196-7
- MathSciNet review: 758196