A modified large-scale structure-preserving doubling algorithm for a large-scale Riccati equation from transport theory

摘要

We consider the large scale nonsymmetric algebraic Riccati equation arisingin transport theory, where the $nimes n$ coefficient matrices $B, C$ aresymmetric and low-ranked and $A, E$ are rank one updates of nonsingulardiagonal matrices. By introducing a balancing strategy and setting appropriateinitial matrices carefully, we can simplify the large-scalestructure-preserving doubling algorithm (SDA_ls) for this special equation. Wegive modified large-scale structure-preserving doubling algorithm, which canreduce the flop operations of original SDA_ls by half. Numerical experimentsillustrate the effectiveness of our method.