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Efficient algorithms for generalized algebraic Bernoulli equations based on the matrix sign function

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Abstract

We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory. Here, we discuss algorithms based on a generalization of the Newton iteration for the matrix sign function. The algorithms are easy to parallelize and provide 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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Correspondence to Sergio Barrachina.

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Barrachina, S., Benner, P. & Quintana-Ortí, E.S. Efficient algorithms for generalized algebraic Bernoulli equations based on the matrix sign function. Numer Algor 46, 351–368 (2007). https://doi.org/10.1007/s11075-007-9143-x

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