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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
Software:
LAPACK
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