Abstract
Abstract This paper an iterative method is presented to solve the minimum Frobenius norm residual problem: min∥AXB − C∥ with unknown symmetric matrix X. By this iterative method, for any initial symmetric matrix X0, 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 ^ to a given matrix X ¯ in Frobenius norm can be obtained by first finding the least norm solution X ∼ ∗ of the new minimum residual problem: min ‖ A X ∼ B - C ∼ ‖ with unknown symmetric matrix X ∼ , where C ∼ = C - A X ¯ + X ¯ T 2 B . Given numerical examples are show that the iterative method is quite efficient.
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