Solution Form and Simple Iteration of a Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory
Solution Form and Simple Iteration of a Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory
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DOI：
10.1137/s0895479801397275
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发表时间：
2005-03
期刊：
影响因子：
--
通讯作者：
Linzhang Lu
中科院分区：
文献类型：
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作者：
Linzhang Lu
我们感兴趣的是计算输运理论中出现的非对称代数Riccati方程的最小正解。我们表明，这种计算可以通过只计算向量方程的最小正解来完成，这是从Riccati方程的特殊形式的解决方案。提出了一种求解矢量方程的简单迭代法。这种简单迭代法比Juang在[Linear Algebra Appl.，230（1995），pp. 89- 100]。最小正解的对称情形和界也被考虑。给出了数值实验。
We are interested in computing the minimal positive solution of a nonsymmetric algebraic Riccati equation arising in transport theory. We show that this computation can be done via computing only the minimal positive solution of a vector equation, which is derived from the special form of solutions of the Riccati equation. A simple iterative method is presented for solving the vector equation. The simple iteration is much more efficient than the Gauss--Jacobi method presented by Juang in [Linear Algebra Appl., 230 (1995), pp. 89--100] for the Riccati equation. The symmetric case and bounds of the minimal positive solution are also considered. Numerical experiments are given.