On The Best Approximate Solutions of The Matrix Equation AXB=C

2011/03/21 by Özdemir, Halim, Sarduvan, Murat
#15A06 #15A09 #15A24 #65F35 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1103.3945

Abstract

Suppose that the matrix equation AXB=C with unknown matrix X is given, where A, B, and C are known matrices of suitable sizes. The matrix nearness problem is considered over the general and least squares solutions of the matrix equation AXB=C when the equation is consistent and inconsistent, respectively. The implicit form of the best approximate solutions of the problems over the set of symmetric and the set of skew-symmetric matrices are established as well. Moreover, some numerical examples are given for the problems considered.

Related

• Generalized matrix nearness problems
• Matrix nearness problems and eigenvalue optimization
• Computational Methods for Linear Matrix Equations
• Numerical solution of a class of quasi-linear matrix equations
• Some considerations in relation to the matrix equation AXB=C