2014•Journal of Northwest Normal UniversityRequires access
The least squares symmetric solutions of the matrix equation with several variables and its optimal approximation
Lei Liu
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Abstract
The least squares symmetric solutions of the matrix equation with several variables are too difficult to be obtained by applying matrices decomposition.An iterative method is presented to solve the least squares symmetric solutions of the linear matrix equation and its convergence is proved.And minimum norm of the least squares symmetric solutions can be obtained by choosing a special kind of initial symmetric matrices.In addition,the unique optimal approximation solutions to the given matrices in Frobenius norm can be obtained.The given numerical examples demonstrate that the iterative methods are quite efficient.