计算数学
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计算数学  2013, Vol. 35 Issue (4): 401-418    DOI:
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求解非对称代数Riccati 方程几个新的预估-校正法
黄娜1, 马昌凤1, 谢亚君2
1. 福建师范大学数学与计算机科学学院, 福州 350007;
2. 福建江夏学院信息系, 福州 350108
SOME PREDICTOR-CORRECTOR-TYPE ITERATIVE SCHEMES FOR SOLVING NONSYMMETRIC ALGEBRAIC RICCATI EQUATIONS ARISING IN TRANSPORT THEORY
Huang Na1, Ma Changfeng1, Xie Yajun2
1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China;
2. Department of Information, Fujian jiangxia University, Fuzhou 350108, China
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摘要 来源于输运理论的非对称代数Riccati 方程可等价地转化成向量方程组来求解. 本文提出了求解该向量方程组的几个预估—校正迭代格式,证明了这些迭代格式所产生的序列是严格单调递增且有上界,并收敛于向量方程 组的最小正解. 最后,给出了一些数值实验,实验结果表明,本文所提出的算法是有效的.
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关键词非对称代数Riccati方程   迭代格式   最小正解   收敛性分析   数值实验     
Abstract: It is as well known that nonsymmetric algebraic Riccati equations arising in transport theory can be translated to vector equations. In this paper, we propose some predictorcorrector-type iterative schemes to solve the vector equations. And we prove that all the sequence generated by the iterative schemes, which converges to the minimal positive solution of the vector equations, are strictly and monotonically increasing and bounded above. In addition, some numerical results are also reported in the paper, which confirm the good theoretical properties of our approach.
Key wordsNonsymmetric algebraic Riccati equation   iterative scheme   minimal positive solution   convergence analysis   numerical experiment   
收稿日期: 2013-04-11;
基金资助:

国家自然科学基金(11071041,11201074) 资助项目;福建省自然科学基金(2013J01006)资助项目。

引用本文:   
. 求解非对称代数Riccati 方程几个新的预估-校正法[J]. 计算数学, 2013, 35(4): 401-418.
. SOME PREDICTOR-CORRECTOR-TYPE ITERATIVE SCHEMES FOR SOLVING NONSYMMETRIC ALGEBRAIC RICCATI EQUATIONS ARISING IN TRANSPORT THEORY[J]. Mathematica Numerica Sinica, 2013, 35(4): 401-418.
 
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