01-13   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Lars Grasedyck:

Singular value bounds for the Cauchy matrix and solutions of Sylvester equations

The singular values of the solution X to the Sylvester equation AX - XB + G = 0 decay exponentially, if the matrix G is of low rank, the spectra of A,B are contained in disjoint triangles and A,B are diagonalisable. This result is obtained by investigation of the Cauchy matrix and can be generalised to a class of hierarchical matrices instead of low rank matrices.

Mathematics Subject Classification (1991): 15A18, 15A24, 65F15

Keywords: Data-sparse approximation, Sylvester equation, low rank matrices, eigenvalue bounds, singular value bounds, Cauchy matrix, hierarchical matrices

Mail an Jens Burmeister
[Thu Feb 19 18:56:35 2009]
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