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Solutions to the generalized Sylvester matrix equations by a singular value decomposition

✍ Scribed by Bin Zhou; Guangren Duan

Book ID: 107504619
Publisher: South China University of Technology and Academy of Mathematics and Systems Science, CAS
Year: 2007
Tongue: English
Weight: 176 KB
Volume: 5
Category: Article
ISSN: 1672-6340
DOI: 10.1007/s11768-006-6113-0

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## Abstract We consider the Sylvester equation __AX__−__XB__+__C__=0 where the matrix __C__∈ℂ^__n__×__m__^ is of low rank and the spectra of __A__∈ℂ^__n__×__n__^ and __B__∈ℂ^__m__×__m__^ are separated by a line. We prove that the singular values of the solution X decay exponentially, that means for