| 矩阵方程的对称解及其逆矩阵的数值解法 |
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| 引用本文： | 谷田叶,黄贤通,严深海.矩阵方程的对称解及其逆矩阵的数值解法[J].应用数学与计算数学学报,2014(4):468-474. |
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| 作者姓名： | 谷田叶 黄贤通 严深海 |
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| 作者单位： | 赣南师范学院数学与计算机科学学院,江西赣州341000 |
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| 基金项目： | 江西省教育厅科技项目资助项目（GJJ10585） |
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| 摘 要： | 基于矩阵方程LS＋SL^T=p,q]求解对称矩阵S,得到了唯一解的充要条件和解的递推计算式,进一步研究了逆矩阵S-1的求法,数值算例说明了递推计算式的正确性.
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| 关 键 词： | 矩阵方程 对称解 逆矩阵 递推计算式 |
Symmetric solutions of matrix equation and numerical solution of its inverse matrix |
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| GU Tian-ye,HUANG Xian-tong,YAN Shen-hai.Symmetric solutions of matrix equation and numerical solution of its inverse matrix[J].Communication on Applied Mathematics and Computation,2014(4):468-474. |
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| Authors: | GU Tian-ye HUANG Xian-tong YAN Shen-hai |
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| Institution: | (College of Mathematics and Computer Science, Gannan Normal University Ganzhou 341000, Jiangxi Province, China) |
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| Abstract: | The symmetric matrix which the solution for the matrix equation LS ＋SL~T=p,q]is given.We obtain the necessary and sufficient conditions of the unique solution for the reconciliation recursive formula.We further study the inverse matrix.The numerical example illustrates the recursive calculation is correct. |
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| Keywords: | matrix equation symmetric solution inverse matrix recursive formula |
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