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Approximation of rank function and its application to the nearest low-rank correlation matrix

✍ Scribed by Shujun Bi, Le Han, Shaohua Pan

Book ID
120703807
Publisher
Springer US
Year
2012
Tongue
English
Weight
414 KB
Volume
57
Category
Article
ISSN
0925-5001

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Existence of a low rank or β„‹-matrix appr
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## Abstract We consider the Sylvester equation __AX__βˆ’__XB__+__C__=0 where the matrix __C__βˆˆβ„‚^__n__Γ—__m__^ is of low rank and the spectra of __A__βˆˆβ„‚^__n__Γ—__n__^ and __B__βˆˆβ„‚^__m__Γ—__m__^ are separated by a line. We prove that the singular values of the solution X decay exponentially, that means for