Least-Squares Solutions of the Matrix Equation AXA= B Over Bisymmetric Matrices and its Optimal Approximation
نویسندگان
چکیده
A real n × n symmetric matrix X = (x i j)n×n is called a bisymmetric matrix if x i j = xn+1− j,n+1−i . Based on the projection theorem, the canonical correlation decomposition and the generalized singular value decomposition, a method useful for finding the least-squares solutions of the matrix equation AXA= B over bisymmetric matrices is proposed. The expression of the least-squares solutions is given. Moreover, in the corresponding solution set, the optimal approximate solution to a given matrix is also derived. A numerical algorithm for finding the optimal approximate solution is also described.
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تاریخ انتشار 2007