Convergence Analysis of the Generalized Alternating Two-Stage Method
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334299Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 936
 Migallon H, Migallon V, Penades J, Alternating two-stage methods for consistent linear system with applications to the parallel solution of Markov chains, Advances in Engineering Software, vol.41, pp.13-21, 2010.
 Neumaier A. New techniques for the analysis of linear interval equations, Linear Algebra Appl., vol.58, pp.273-325, 1984.
 Ortega JM, Rheinboldt WC, Tterative solution of nonlinear equations in several variables, New York and London:Academic Press,1970.
 Berman A, Plemmons RJ. Nonnegative matrices in the mathematical sciences 3rd ed. New York:Academic Press,1979. Reprinted by SIAM, Philadelphia,1994.
 Frommer A, Szyld DB. H-splittings and two-stage iterative methods. Number Math, vol.63, pp.345-356,1992.
 Varga RS. Matrix iterative analysis, Englewood Cliffs, New Jersey: PrenticeHall,1962.
 Joan-Josep Climent, Carmen Perea. Convergence and comparison theorem for a generalized alternating iterative method. Applied Mathematics and Computation, vol.143, pp.1-14, 2003.
 Robert F, Charnay M,Musy F.Iterations chaotiques serie-parallele pour desequations non-lineaires de point fixe. Appl. Math., vol.20, pp.1-38, 1975.