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

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.