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- W2357255908 abstract "In this paper,the concept of gradient matrix(F(X)) is presented,and an algorithm is constructed to solve the symmetric solution of the minimum Frobenius norm residual problem:min‖(A1XB1,A2XB2)-(C1,C2)‖.By this algorithm,for any initial symmetric matrix X1,a solution X* can be obtained within finite iteration steps in the absence of roundoff errors,and the solution X* with least norm can be obtained by choosing a special kind of initial symmetric matrix.In addition,the unique optimal approximation solution X^ for a given matrix X0 in the Frobenius norm can be obtained by finding the least norm symmetric solution X～* of the new minimum residual problem:min‖(A1X～B1,A2X～B2)-(C～1,C～2)‖,where C～1=C1-A1X0B1,C～2=C2-A2X0B2." @default.
- W2357255908 created "2016-06-24" @default.
- W2357255908 creator A5073574798 @default.
- W2357255908 date "2007-01-01" @default.
- W2357255908 modified "2023-09-24" @default.
- W2357255908 title "An Iterative Method for the Least Squares Symmetric Solution of the Matrix Equations A_1XB_1=C_1,A_2XB_2=C_2 and Its Optimal Approximation" @default.
- W2357255908 hasPublicationYear "2007" @default.
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