MINIMIZATION PROBLEM FOR SYMMETRIC ORTHOGONAL ANTI-SYMMETRIC MATRICES

摘要

By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution X, which is both a least-squares symmetric orthogonal anti-symmetric solution of the matrix equation A~T XA = B and a best approximation to a given matrix X~*. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.