MCG Algorithm for Symmetric Solutions of a Class of Generalized Coupled Sylvester Equations
A modified conjugate gradient algorithm(MCG algorithm)was established in founding the symmetric solution of the generalized coupled Sylvester equation system.We give the properties and convergence proof of the MCG algorithm.When we ignore round off error,the MCG algorithm established in this paper can obtain the symmetric solution of the equation system after finite step iteration.When we select a special initial matrix,the minimum norm symmetric solution of the system of equations can be obtained.Given a known matrix,we can find the best approximation matrix for this matrix from a set of known solution matrices.Numerical experiments verify the feasibility of the algorithm proposed in the paper.
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