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- W2024384195 abstract "We consider the Sylvester equation AX−XB+C=0 where the matrix C∈ℂn×m is of low rank and the spectra of A∈ℂn×n and B∈ℂm×m are separated by a line. We prove that the singular values of the solution X decay exponentially, that means for any ε∈(0,1) there exists a matrix X̃ of rank k=O(log(1/ε)) such that ∥X−X̃∥2⩽ε∥X∥2. As a generalization we prove that if A,B,C are hierarchical matrices then the solution X can be approximated by the hierarchical matrix format described in Hackbusch (Computing 2000; 62: 89–108). The blockwise rank of the approximation is again proportional to log(1/ε). Copyright © 2004 John Wiley & Sons, Ltd." @default.
- W2024384195 created "2016-06-24" @default.
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- W2024384195 date "2004-04-19" @default.
- W2024384195 modified "2023-09-26" @default.
- W2024384195 title "Existence of a low rank or ℋ︁-matrix approximant to the solution of a Sylvester equation" @default.
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- W2024384195 doi "https://doi.org/10.1002/nla.366" @default.
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