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In this paper we propose a parallel two-stage iteration algorithm for solving large-scale continuous Sylvester equations. By splitting the coefficient matrices, the original linear system is transformed into a symmetric linear system which is then solved by using the SYMMLQ algorithm. In order to improve the relative parallel efficiency, an adjusting strategy is explored during the iteration calculation of the SYMMLQ algorithm to decrease the degree of the reduce-operator from two to one communications at each step. Moreover, the convergence of the iteration scheme is discussed, and finally numerical results are reported showing that the proposed method is an efficient and robust algorithm for this class of continuous Sylvester equations on a parallel machine.

A Parallel Two-Stage Iteration Method for Solving Continuous Sylvester Equations