Least Squares Solution of BXA T = T over Symmetric, Skew-Symmetric, and Positive Semidefinite X
Yuanbei Deng, Xi-Yan Hu, Lei Zhang · SIAM Journal on Matrix Analysis and Applications · 2003
An efficient method based on the quotient singular value decomposition (QSVD) is used to solve the constrained least squares problem $\min \| T-BXA^T\|_F$ over symmetric, skew-symmetric, and positive semidefinite (maybe asymmetrical) X. The general expression of the solution is given and some necessary and sufficient conditions are derived about the solvability of the matrix equation BXA T =T. In each case, an algorithm is given for the unique solution when B and A are of full column rank.