The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation (Q949300)
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scientific article; zbMATH DE number 5354630
| Language | Label | Description | Also known as |
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| English | The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation |
scientific article; zbMATH DE number 5354630 |
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The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation (English)
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21 October 2008
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Given the linear matrix equation \(A^T XA = B\), by using the generalized singular value decomposition, this paper deals with (1) the necessary and sufficient conditions for the existence of the anti-symmetric ortho-symmetric solution \(X\), and (2) the existence and uniqueness of its optimal approximation \(X^*\) satisfying \(\min_X \| X - X^*\| \). Finally, numerical methods of the optimal approximation are formulated and illustrative numerical experiments are presented.
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matrix equation
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anti-symmetric ortho-symmetric solution
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optimal approximation
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singular value decomposition
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numerical experiments
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