求解非对称代数Riccati方程几个新的预估-校正法  

SOME PREDICTOR-CORRECTOR-TYPE ITERATIVE SCHEMES FOR SOLVING NONSYMMETRIC ALGEBRAIC RICCATI EQUATIONS ARISING IN TRANSPORT THEORY

作　　者：黄娜[1] 马昌凤[1] 谢亚君[2] 

机构地区：[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

出　　处：《计算数学》2013年第4期401-418,共18页Mathematica Numerica Sinica

基　　金：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

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.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 predictor- corrector-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.

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 

分 类 号：O241.8[理学—计算数学]