On the Doubling Algorithm for a (Shifted) Nonsymmetric Algebraic Riccati Equation
On the Doubling Algorithm for a (Shifted) Nonsymmetric Algebraic Riccati Equation
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DOI：
10.1137/060660837
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发表时间：
2007-11
期刊：
影响因子：
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通讯作者：
Chun-Hua Guo;B. Iannazzo;B. Meini
中科院分区：
文献类型：
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作者：
Chun-Hua Guo;B. Iannazzo;B. Meini
研究了四系数矩阵构成不可约矩阵的非对称代数Riccati方程。重点讨论了在马尔可夫模型研究中出现的不可约奇异矩阵M$的情况。考虑用加倍算法求最小非负解，这是一个有实际意义的算法。对于$M$是一个非奇异$M$-矩阵的情况，该算法最近已被其他人研究。提出了一种移位技术，将原里卡蒂方程转化为由四个系数矩阵构成非奇异矩阵的新里卡蒂方程。将加倍算法应用于位移Riccati方程时，其收敛速度加快。
Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible $M$-matrix $M$ are considered. The emphasis is on the case where $M$ is an irreducible singular $M$-matrix, which arises in the study of Markov models. The doubling algorithm is considered for finding the minimal nonnegative solution, the one of practical interest. The algorithm has been recently studied by others for the case where $M$ is a nonsingular $M$-matrix. A shift technique is proposed to transform the original Riccati equation into a new Riccati equation for which the four coefficient matrices form a nonsingular matrix. The convergence of the doubling algorithm is accelerated when it is applied to the shifted Riccati equation.