A modified gradient based algorithm for solving Sylvester equations (Q426622)
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scientific article; zbMATH DE number 6045323
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A modified gradient based algorithm for solving Sylvester equations |
scientific article; zbMATH DE number 6045323 |
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A modified gradient based algorithm for solving Sylvester equations (English)
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11 June 2012
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\textit{Ding} and \textit{Chen} proposed a gradient based algorithm (GI algorithm) to solve the Sylvester equation \(AX+XB=C\) [IEEE Trans. Auto. Control 50, 1216--1221 (2005)]. The convergence rate of this algorithm is slow and stagnation will happen for an ill-conditioned problem. In the present paper, a modified GI algorithm is presented. The basic idea is that the information generated in the first half-iterative step is fully exploited to construct an approximate solution in the second half-iterative step. The optimal convergence factor is explicitly presented. Numerical results show that the modified GI algorithm is efficient and robust.
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Sylvester equation
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gradient based method
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convergence factor
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algorithm
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ill-conditioned problem
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numerical results
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