Abstract
For solving the matrix equation Ax=b, with coefficient matrix being the identity plus the skew-symmetric part ofA, a variety of extrapolated iterative methods are reported. These methods using an optimum extrapolation parameter are able to give a better asymptotic convergence rate. In this paper we propose an, iterative method without the parameter estimation.
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References
M. eiermann, W. Niethammer and R.S. Varga, Acceleration of relaxation method for non-Hermitian linear systems. SIAM J. Matrix Anal. Appl.,13, (1992) 979–991.
N. Gaitanos, A. Hadjidimos and A. Yeyios, Optimum accelerated overrelaxation (AOR) method for systems with positive coefficient matrix. SIAM J. Numer. Anal.,12 (1983), 774–783.
H.M. Neuman and R.S. Varga, On the sharpness of some upper bounds for the spectral radii of S.O.R. iteration matrices. Numer. Math.,35 (1980), 69–79.
W. Niethammer and J. Schade, On a relaxed SOR-method applied to nonsymmetric linear systems. J. Comput. Appl. Math.,1 (1975), 133–136.
W. Niethammer, On Different Splitting and the Associated Iteration Methods. SIAM J. Numer. Anal.,16 (1979), 186–200.
R.S. Varga, Extensions of the successive overrelaxation theory with applications to finite element approximations. Topics in Numerical Analysis (ed J.J.H. Miller), Academic Press, New York, 1973, 329–343.
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Kinashi, Y., Sawami, H. & Niki, H. An iterative method applied to nonsymmetric linear systems. Japan J. Indust. Appl. Math. 13, 235–241 (1996). https://doi.org/10.1007/BF03167245
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DOI: https://doi.org/10.1007/BF03167245