不相容矩阵不等式AX≥B的最小偏差对称解  

The smallest deviation symmetric solutions of the inconsistent matrix inequality AX≥B

作　　者：彭靖静[1] 段复建[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2013年第2期169-172,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11261014;11101100);广西自然科学基金(2011GXNSFA018138)

摘　　要：提出了求解不相容矩阵不等式AX≥B的最小非负偏差对称解的一种迭代方法。该迭代方法可以计算相容矩阵方程AX=B和相容矩阵不等式AX≥B的对称解。证明了迭代方法的收敛性,通过数值例子说明了算法的有效性。An iteration method to compute the smallest deviation symmetric solutions of the inconsistent matrix inequality AX≥B is proposed. The presented iteration method can be also used to compute the symmetric solutions of the matrix equation AX≥B and the consistent matrix inequality AX≥B. The convergence of the iterative method is proved. The efficiency of the algorithm is illustrated by numerical experiment.

关 键 词：矩阵方程 矩阵不等式 迭代方法 最小二乘问题 

分 类 号：O241.6[理学—计算数学]