A modified structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equations from transport theory

Abstract

We consider the nonsymmetric algebraic Riccati equation arising in transport theory, where the n×n coefficient matrices A,B,C and E involved in the equation are rank structured. After a balancing strategy the matrix X̃T is the minimal positive solution of the dual algebraic Riccati equation, we can simplify the structure-preserving doubling algorithm (SDA) to this special equation and give a modified SDA, which has less computational cost at each iteration step. Also, we use numerical experiments to show the effectiveness of our new methods.