| 矩阵方程AXB＋CX^T D=F自反最小二乘解的迭代算法 |
| |
| 引用本文： | 袁飞,张凯院.矩阵方程AXB＋CX^T D=F自反最小二乘解的迭代算法[J].数值计算与计算机应用,2009,30(3):195-201. |
| |
| 作者姓名： | 袁飞 张凯院 |
| |
| 作者单位： | 西北工业大学应用数学系,西安,710072 |
| |
| 基金项目： | 陕西省自然科学基金资助项目 |
| |
| 摘 要： | 建立了求矩阵方程AXB＋CX^TD=F的自反最小二乘解的迭代算法,证明了迭代算法的收敛性,该算法能够在有限步迭代计算之后得到矩阵方程的一个自反最小二乘解,或者极小范数自反最小二乘解。另外,还给出了在解集合中对给定矩阵的最佳逼近。
|
| 关 键 词： | 矩阵方程 自反矩阵 最小二乘解 极小范数解 迭代算法 最佳逼近 |
AN ITERATIVE METHOD FOR THE LEAST SQUARES REFLEXIVE MATRIX SOLUTION OF MATRIX EQUATION AXB + CXTD = F |
| |
| Yuan Fei,Zhang Kaiyuan.AN ITERATIVE METHOD FOR THE LEAST SQUARES REFLEXIVE MATRIX SOLUTION OF MATRIX EQUATION AXB + CXTD = F[J].Journal on Numerical Methods and Computer Applications,2009,30(3):195-201. |
| |
| Authors: | Yuan Fei Zhang Kaiyuan |
| |
| Affiliation: | Yuan Fei Zhang Kaiyuan (Dept. of Applied Mathematics, Northwestern Polytechnical University, Xi ＇ an 710072, China) |
| |
| Abstract: | An iterative method is presented to find the least squares reflexive matrix solution of the matrix equation AXB＋CX^TD = F.The convergence of the iterative method is proved.By this iterative method,its least squares reflexive matrix solution or least-norm least squares reflexive matrix solution can be got within finite steps.In addition,its optimal approximation solution to a given matrix in a given reflexive matrix solution set can be obtained. |
| |
| Keywords: | matrix equation reflexive matrix least squares solution least-norm solution iterative method optimal approximation |
| 本文献已被 维普 万方数据 等数据库收录！ |
|
