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Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign FunctionBarrachina, Sergio, Benner, Peter, Quintana-Ortí, Enrique S. 11 September 2006 (has links) (PDF)
We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory in the context of stabilization of linear dynamical systems, coprime factorization of rational matrix-valued functions, and model reduction. The algorithms we propose, based on a generalization of the Newton iteration for the matrix sign function, are easy to parallelize, yielding an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.
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Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign FunctionBarrachina, Sergio, Benner, Peter, Quintana-Ortí, Enrique S. 11 September 2006 (has links)
We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory in the context of stabilization of linear dynamical systems, coprime factorization of rational matrix-valued functions, and model reduction. The algorithms we propose, based on a generalization of the Newton iteration for the matrix sign function, are easy to parallelize, yielding an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.
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