Parallel Distributed Solvers for Large Stable Generalized Lyapunov Equations

In this paper we study the solution of stable generalized Lyapunov matrix equations with large-scale, dense coefficient matrices. Our iterative algorithms, based on the matrix sign function, only require scalable matrix algebra kernels which are highly efficient on parallel distributed architectures. This approach avoids therefore the difficult parallelization of direct methods based on the QZ algorithm. The experimental analtsis reports a remarkable performance of our solvers on an IBM SP2 platform.

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