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Verified bounds for all the singular values of matrix. (English) Zbl 1312.65062

The author proposes four algorithms for computing verified bounds of all the singular values of a matrix and shows that these algorithms give equal or tighter bounds, as well as smaller computational costs than those proposed in some previous papers. Numerical results concerning generalized singular values are also presented.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A18 Eigenvalues, singular values, and eigenvectors
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65G20 Algorithms with automatic result verification
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