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Gradient-based maximal convergence rate iterative method for solving linear matrix equations. (English) Zbl 1188.65058
This paper deals with a gradient-based iterative methed proposed by Ding and Chen [IEEE Trans. Automat. Control. 50(8), 1216–1221 (2005)] for solving a class of linear matrix equation. The main contribution of this paper is that it is shown explicitly how to choose the convergence factor such that the convergence rate of the algorithm is maximized and analytical expression of the maximal convergence rate is given. These results shed some light on studying gradient-based algorithm reported in the literature by using control system theory.

MSC:
65F30 Other matrix algorithms (MSC2010)
65F10 Iterative numerical methods for linear systems
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
15A09 Theory of matrix inversion and generalized inverses
15A12 Conditioning of matrices
15A24 Matrix equations and identities
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