Iterative Algorithm for the Optimal Approximation Solution of Matrix Equations AXB+CXTD=E with Generalized Constraint

doi:10.13438/j.cnki.jdzk.2025.01.001

Abstract

Abstract: An iterative algorithm is presented to calculate the optimal approximation solution of the matrix equations AXB+CX^TD=E with constraint conditions GX=H.It is proved that given a special initial matrix satisfying the generalized constraints,the minimal norm least squares solution of the matrix equation under the generalized constraints can be obtained by the finite-order iterative algorithm,and the optimal approximation solution can be calculated by using the minimal norm least squares solution.

Key words: minimal norm least squares solution, optimal approximation solution, iterative algorithm, gradient projection

YANG Jiawen, WAN Peng, LIANG Jinrong. Iterative Algorithm for the Optimal Approximation Solution of Matrix Equations AXB+CX^TD=E with Generalized Constraint [J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(1): 1-11.

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Iterative Algorithm for the Optimal Approximation Solution of Matrix Equations AXB+CX^TD=E with Generalized Constraint

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