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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:
65F30Other matrix algorithms
65F10Iterative methods for linear systems
65N22Solution of discretized equations (BVP of PDE)
15A09Matrix inversion, generalized inverses
15A12Conditioning of matrices
15A24Matrix equations and identities