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| 摘要: |
| 本文研究了矩阵方程X + A*X-αA + B*X-βB=I 在α,β∈(0, 1] 时的正定解. 利用单调有界极限存在准则, 构造三种迭代算法, 获得了方程的正定解, 拓宽了此类方程的求解方法. 数值算例说明算法的可行性. |
| 关键词: 矩阵方程 正定解 迭代方法 |
| DOI： |
| 分类号:O241.7 |
| 基金项目: |
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| ON THE POSITIVE DEFINITE SOLUTION OF MATRIX EQUATION X + A*X-αA + B*X-βB = I |
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CUI Xiao-mei,LIU Li-bo,GAO Han
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| Abstract: |
| The positive definite solutions of the matrix equation X + A*X-αA + B*X-βB = I,α,β∈(0, 1] are investigated in this paper. By using monotone bounded limit existence criteria, three iterative algorithms are constructed to obtain the positive definite solution which widen the solution of such equation. Numerical examples are given to illustrate the effectiveness of the methods. |
| Key words: matrix equation positive definite solution iterative methods |
