Solvability of some constrained matrix approximation problems using core-EP inverses
Solvability of some constrained matrix approximation problems using core-EP inverses
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DOI：
10.1007/s40314-020-01360-y
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发表时间：
2020-11
影响因子：
2.6
通讯作者：
D. Mosić;P. Stanimirović;V. Katsikis
中科院分区：
文献类型：
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作者：
D. Mosić;P. Stanimirović;V. Katsikis
利用CORE-EP逆，我们得到了约束矩阵极小化问题在欧氏范数下的唯一解：，约束在哪里，和。对于指数为1的复矩阵和非奇异复矩阵，这个问题归结为众所周知的结果。我们给出了两种求上述问题唯一解的Cramer规则，应用了一个著名的公式和一个新的核心-EP逆的公式。此外，我们还考虑了相应的约束矩阵逼近问题及其基于加权核心-EP逆的Cramer规则。给出了求解线性等式约束最小二乘问题的经典策略的数值比较。讨论了所考虑的约束优化问题的特殊情况及其在求解约束矩阵方程中的应用。
Using the core-EP inverse, we obtain the unique solution to the constrained matrix minimization problem in the Euclidean norm:, subject to the constraintwhere,and. This problem reduces to well-known results for complex matrices of index one and for nonsingular complex matrices. We present two kinds of Cramer’s rules for finding unique solution to the above mentioned problem, applying one well-known expression and one new expression for core-EP inverse. Also, we consider a corresponding constrained matrix approximation problem and its Cramer’s rules based on theW-weighted core-EP inverse. Numerical comparison with classical strategies for solving the least squares problems with linear equality constraints is presented. Particular cases of the considered constrained optimization problem are considered as well as application in solving constrained matrix equations.