Performance enhancement of doubling algorithms for a class of complex nonsymmetric algebraic Riccati equations

A new class of complex nonsymmetric algebraic Riccati equations has been studied by Liu & Xue (2012, SIAM J. Matrix Anal. Appl., 33, 569–596), which is related to the M-matrix algebraic Riccati equations. Doubling algorithms, with properly chosen parameters, are used there for equations in this new class. It is pointed out that the number of iterations for the doubling algorithms may be relatively large in some situations. In this paper, we show that the performance of the doubling algorithms can often be improved significantly if a proper preprocessing procedure is used on the given Riccati equation. There are some difficult cases for which the preprocessing procedure does not help much by itself. We then propose new strategies for choosing parameters for doubling algorithms after using the preprocessing procedure. Numerical experiments show that our preprocessing procedure and the new parameter strategies are very effective.