Numerical solutions of AXB = C for mirrorsymmetric matrix X under a specified submatrix constraint

Abstract

Mirrorsymmetric matrices, which are the iteraction matrices of mirrorsymmetric structures, have important application in studying odd/even-mode decomposition of symmetric multiconductor transmission lines (MTL). In this paper we present an efficient algorithm for minimizing $${\|AXB-C\|}$$where $${\|\cdot\|}$$is the Frobenius norm, $${A\in \mathbb{R}^{m\times n}}$$, $${B\in \mathbb{R}^{n\times s}}$$, $${C\in \mathbb{R}^{m\times s}}$$and $${X\in \mathbb{R}^{n\times n}}$$is mirrorsymmetric with a specified central submatrix [x ij ]r≤i, j≤n-r . Our algorithm produces a suitable X such that AXB = C in finitely many steps, if such an X exists. We show that the algorithm is stable any case, and we give results of numerical experiments that support this claim.