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