In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.<\/p>\r\n","references":"[1] Migallon H, Migallon V, Penades J, Alternating two-stage methods for\r\nconsistent linear system with applications to the parallel solution of\r\nMarkov chains, Advances in Engineering Software, vol.41, pp.13-21,\r\n2010.\r\n[2] Neumaier A. New techniques for the analysis of linear interval equations,\r\nLinear Algebra Appl., vol.58, pp.273-325, 1984.\r\n[3] Ortega JM, Rheinboldt WC, Tterative solution of nonlinear equations in\r\nseveral variables, New York and London:Academic Press,1970.\r\n[4] Berman A, Plemmons RJ. Nonnegative matrices in the mathematical\r\nsciences 3rd ed. New York:Academic Press,1979. Reprinted by SIAM,\r\nPhiladelphia,1994.\r\n[5] Frommer A, Szyld DB. H-splittings and two-stage iterative methods.\r\nNumber Math, vol.63, pp.345-356,1992.\r\n[6] Varga RS. Matrix iterative analysis, Englewood Cliffs, New Jersey:\r\nPrenticeHall,1962.\r\n[7] Joan-Josep Climent, Carmen Perea. Convergence and comparison theorem\r\nfor a generalized alternating iterative method. Applied Mathematics and\r\nComputation, vol.143, pp.1-14, 2003.\r\n[8] Robert F, Charnay M,Musy F.Iterations chaotiques serie-parallele pour\r\ndesequations non-lineaires de point fixe. Appl. Math., vol.20, pp.1-38,\r\n1975.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 33, 2009"}