In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.<\/p>\r\n","references":"[1] A. Hadjidimos and A. Yesios, The principle of extrapolation in connection\r\nwith the accelerated overrelaxion method, Linear Algebra Appl., vol.30,\r\npp.115-128, 1980.\r\n[2] D. Wang, On the convergence of parallel multisplitting AOR algorithm,\r\nLinear Algebra Appl., vol.154-156, pp.473-486, 1991.\r\n[3] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical\r\nSciences, Academic Press, New York,1979.\r\n[4] A. Neumaier, On the Comparison of H-matrices with M-matrices, Linear\r\nAlgebra Appl., vol.83, pp.135-141, 1986.\r\n[5] A. Frommer and D. B. Szyld, H-splittings and two-stage iterative methods,\r\nNumer Math., vol.63, pp.345-356, 1992.\r\n[6] Y. Z. Song and L. Wang, On the semiconvergence of extrapolated iterative\r\nmethods for singular linear systems, Appl. Numer. Math., vol.44, pp.401-\r\n413, 2003.\r\n[7] C. L. Wang and L. C. Zhang, Parallel Multisplitting Algorithms for\r\nSingular H-matrices, Numerical Mathematics(a Journal of Chinese Universities)(\r\nin Chinese), vol.1, pp.10-15, 2000.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 43, 2010"}