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An Iterative Algorithm for Solving the Least-Squares Problem of Matrix Equation AXB+CYD=E
Kai-juan Shen,Chuan-hua You,Yu-xia Du 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.5
In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB + CY D = E over un-known matrix pair [X, Y ]. By this iterative method, for any initial matrix pair [X1, Y1], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [X0, Y0] in Frobenius norm. Given numerical examples show that the algorithm is efficient. In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB + CY D = E over un-known matrix pair [X, Y ]. By this iterative method, for any initial matrix pair [X1, Y1], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [X0, Y0] in Frobenius norm. Given numerical examples show that the algorithm is efficient.
AN ITERATIVE ALGORITHM FOR SOLVING THE LEAST-SQUARES PROBLEM OF MATRIX EQUATION AXB+CYD=E
Shen, Kai-Juan,You, Chuan-Hua,Du, Yu-Xia Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.5
In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB+CYD=E over unknown matrix pair [X, Y]. By this iterative method, for any initial matrix pair [$X_1,\;Y_1$], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [$X_0,\;Y_0$] in Frobenius norm. Given numerical examples show that the algorithm is efficient.