Solving stable generalized Lyapunov equations with the matrix sign function (Q1293734)
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scientific article; zbMATH DE number 1310135
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solving stable generalized Lyapunov equations with the matrix sign function |
scientific article; zbMATH DE number 1310135 |
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Solving stable generalized Lyapunov equations with the matrix sign function (English)
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29 June 1999
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Using the sign function method, the Lyapunov equation \(Q+ A^TXE+ E^TXA= O\), \(X= X^T\) is being studied. The eigenvalues of the pencil \(A-\lambda E\) are assumed to be contained in the open left-half plane. Several results from earlier studies with \(E= I\) are extended to the general case. A new stopping criterion is introduced which saves computational cost/work space compared to the existing criteria for sign function iterations.
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Lyapunov matrix equation
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matrix sign function
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Newton iteration
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Riccati matrix equation
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