We propose a method of Lanczos type for solving a linear system with a normal matrix whose spectrum is contained in a second-degree curve. This is a broader class of matrices than that of the (l, m)-normal matrices in...
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We propose a method of Lanczos type for solving a linear system with a normal matrix whose spectrum is contained in a second-degree curve. This is a broader class of matrices than that of the (l, m)-normal matrices introduced in a recent paper by Barth and Manteuffel. Our approach is similar to that of Huhtanen in the sense that both use the condensed form of normal matrices discovered by Elsner and Ikramov. However, there are a number of differences, among which are: (i) our method is modeled after the symmlq algorithm of Paige and Saunders;(11) it uses only one matrix-vector product per step;(iii) we provide effective means for monitoring the size of the residual during the process. Numerical experiments are presented.
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 symmetr...
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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.
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