Abstract
We investigate the numerical solution of algebraic Bernoulli equations (ABE) via the Newton iteration for the matrix sign function. Bernoulli equations are nonlinear matrix equations arising in control and systems theory in the context of stabilisation of linear systems, coprime factorisation of rational matrix-valued functions, as well as model reduction. The algorithm proposed here is easily parallelisable and thus provides an efficient tool to solve large-scale problems. We report the parallel performance and scalability of our parallel implementations on a cluster of Intel Xeon processors.
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