Matrix equations and structures: efficient solution of special discrete algebraic Riccati equations

摘要

We propose a new quadratically convergent algorithm, having a low computational cost per step and good numerical stability properties, that allows the computation of the maximal solutions of the matrix equations X + C{sup}*X{sup}-1C = Q, X -C{sup}*X{sup}-1C = Q, X + C{sup}*(R + B{sup}*XB){sup}-1C = Q. The algorithm is based on the cyclic reduction method.