Nonsymmetric Algebraic Riccati Equations and Wiener-Hopf Factorization for M-Matrices
Nonsymmetric Algebraic Riccati Equations and Wiener-Hopf Factorization for M-Matrices
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DOI：
10.1137/s0895479800375680
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Chun-Hua Guo
中科院分区：
文献类型：
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作者：
Chun-Hua Guo
本文考虑四个系数矩阵构成一个M-矩阵的非对称代数Riccati方程。这种类型的非对称代数黎卡提方程出现在应用概率论和输运理论中。用牛顿法和基本不动点迭代法可以求出这些方程的最小非负解。对这些方程的研究也与M-矩阵的Wiener-Hopf分解密切相关。我们解释了如何找到最小非负解的Schur方法和比较Schur方法与牛顿法和一些基本的不动点迭代。本文的发展平行于线性二次控制中的对称代数Riccati方程。
We consider the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M-matrix. Nonsymmetric algebraic Riccati equations of this type appear in applied probability and transport theory. The minimal nonnegative solution of these equations can be found by Newton's method and basic fixed-point iterations. The study of these equations is also closely related to the so-called Wiener--Hopf factorization for M-matrices. We explain how the minimal nonnegative solution can be found by the Schur method and compare the Schur method with Newton's method and some basic fixed-point iterations. The development in this paper parallels that for symmetric algebraic Riccati equations arising in linear quadratic control.