Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations
Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations
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DOI：
10.1002/nla.500
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发表时间：
2006-10
影响因子：
4.3
通讯作者：
Z. Bai;Xiao-Xia Guo;Shufang Xu
中科院分区：
文献类型：
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作者：
Z. Bai;Xiao-Xia Guo;Shufang Xu
对于非对称代数Riccati方程，我们通过交替分裂和连续逼近代数Riccati算子的技术结合，建立了一类计算其最小非负解的交替线性化隐式（ALI）迭代方法。这些方法都包含一个迭代参数，该参数的合理选择可以使迭代方法快速收敛。在适当的条件下，证明了ALI迭代矩阵序列的单调收敛性，并估计了其渐近收敛因子。数值实验表明，ALI迭代方法是可行和有效的，优于牛顿迭代法和不动点迭代法。此外，我们进一步推广了已知的不动点迭代，得到了求解非对称代数Riccati方程的一类广泛的松弛分裂迭代方法。版权所有©2006约翰威利父子有限公司
For the non‐symmetric algebraic Riccati equations, we establish a class of alternately linearized implicit (ALI) iteration methods for computing its minimal non‐negative solutions by technical combination of alternate splitting and successive approximating of the algebraic Riccati operators. These methods include one iteration parameter, and suitable choices of this parameter may result in fast convergent iteration methods. Under suitable conditions, we prove the monotone convergence and estimate the asymptotic convergence factor of the ALI iteration matrix sequences. Numerical experiments show that the ALI iteration methods are feasible and effective, and can outperform the Newton iteration method and the fixed‐point iteration methods. Besides, we further generalize the known fixed‐point iterations, obtaining an extensive class of relaxed splitting iteration methods for solving the non‐symmetric algebraic Riccati equations. Copyright © 2006 John Wiley & Sons, Ltd.