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Solving stable generalized Lyapunov equations with the matrix sign function. (English) Zbl 0940.65035
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.

##### MSC:
 65F10 Iterative numerical methods for linear systems 15A24 Matrix equations and identities
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