Some accelerated iterative algorithms for solving nonsymmetric algebraic Riccati equations arising in transport theory

Abstract

In this paper, some accelerated iterative algorithms are developed to find the minimal positive solution of the nonsymmetric algebraic Riccati equation arising in transport theory. The convergence analysis shows that the sequences of vectors generated by iterative algorithms with the initial vector are monotonically increasing and converge to the minimal positive solution of the vector equations. Numerical examples are provided to illustrate the efficiency of the proposed algorithms and testify the conclusions suggested in this paper.