Perturbation analysis for the matrix equation \(X - \sum^m_{i=1} A^\ast_i XA_i + \sum^n_{j=1} B^\ast_j XB_j = I\) (Q1952939)
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scientific article; zbMATH DE number 6169977
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Perturbation analysis for the matrix equation \(X - \sum^m_{i=1} A^\ast_i XA_i + \sum^n_{j=1} B^\ast_j XB_j = I\) |
scientific article; zbMATH DE number 6169977 |
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Perturbation analysis for the matrix equation \(X - \sum^m_{i=1} A^\ast_i XA_i + \sum^n_{j=1} B^\ast_j XB_j = I\) (English)
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3 June 2013
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Summary: We consider the perturbation analysis of the matrix equation \(X - \sum^m_{i=1} A^\ast_i XA_i + \sum^n_{j=1} B^\ast_j XB_j = I\). Based on the matrix differentiation, we first give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the sharpness of the perturbation bound.
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perturbation analysis
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matrix equation
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matrix differentiation
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perturbation bound
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positive definite solution
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numerical example
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