非对称代数Riccati方程的一种快速Newton型算法

A fast Newton-type method for solving a class of nonsymmetric algebraic Riccati equation

对于运输理论中所产生的一类非对称代数Riccati方程,给出了一种新的快速迭代算法,该算法是基于一种具有三阶收敛性的两步Newton法而得到,并证明了该算法所产生的向量序列的单调收敛性.数值实验显示该算法具有比另外两种Newton型法更好的收敛行为.

For a class of nonsymmetric algebra Riccati equation arising from transport theory,the present paper proposes a new fast iterative algorithm based on a two-step Newton-typemethod with third-order convergence.Then,themonotone convergence of the sequence generated by the algorithm is proved.Numerical experiments show that this algorithm has better convergence behavior than the other two Newton-type methods.