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Low rank solution of data-sparse Sylvester equations

โœ Scribed by U. Baur


Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
145 KB
Volume
15
Category
Article
ISSN
1070-5325

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โœ L. Grasedyck ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 190 KB

## Abstract We consider the Sylvester equation __AX__โˆ’__XB__+__C__=0 where the matrix __C__โˆˆโ„‚^__n__ร—__m__^ is of low rank and the spectra of __A__โˆˆโ„‚^__n__ร—__n__^ and __B__โˆˆโ„‚^__m__ร—__m__^ are separated by a line. We prove that the singular values of the solution X decay exponentially, that means for

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A recently developed compression and sparse solution strategy for electromagnetic problems is applied to integral-equation formulations of scattering from perfectly conducting targets in three dimensions. It is shown that the resulting representations of both the impedance matrix and its inverse are