Abstract
A class of first order factorization methods for the solution of large, symmetric, sparse systems of equations is introduced. Asymptotic results for the computational complexity are developed, results from numerical experiments are presented and comparisons with other iterative and direct methods are carried out.
Similar content being viewed by others
References
I. Gustafsson,A class of first order factorization methods, Computer Sciences 77.04R, Chalmers University of Technology, Göteborg, Sweden, (1977).
O. Axelsson,A class of iterative methods for finite element equations, Comp.meth. in appl. mechanics and engineering 9 (1976), 123–137.
O. Axelsson,On preconditioning and convergence acceleration in sparse matrix problems, CERN 74-10, Genève, Switzerland (1974).
J. A. Meijerink and H. A. van der Vorst,An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. of Comp. 31 (1977), 148–162.
P. Saylor,Second order strongly implicit symmetric factorization methods for the solution of elliptic difference equations, SIAM J. Numer. Anal. 11 (1974), 894–908.
H. L. Stone,Iterative solution of implicit approximations of multidimensional partial differential equations, SIAM J. Numer. Anal. 5 (1968), 530–558.
T. Dupont, R. Kendall and H. H. Rachford Jr.,An approximate factorization procedure for solving selfadjoint elliptic difference equations, SIAM J. Numer. Anal. 5 (1968), 559–573.
O. Axelsson,A generalized SSOR method, BIT 12 (1972), 443–467.
I. Gustafsson,On first order factorization methods for the solution of problems with mixed boundary conditions and problems with discontinuous material coefficients, Computer Sciences 77.13R, Chalmers University of Technology, Göteborg, Sweden (1977).
A. George,Nested dissection of a regular finite element mesh, SIAM J. Numer. Anal. 10 (1973), 345–363.
A. George,Numerical experiments using dissection methods to solve n by n grid problems, Research Report CS-75-07, University of Waterloo, Canada (1975).
H. M. Markowitz,The elimination form of the inverse and its applications to linear programming, Management Sci. (1957), 255–269.
O. Axelsson and I. Gustafsson,A modified upwind scheme for convective transport equations and the use of a conjugate gradient method for the solution of non-symmetric systems of equations, Computer Sciences 77.12R, Chalmers University of Technology, Göteborg, Sweden (1977).
O. Axelsson, and I. Gustafsson,Iterative methods for the solution of the Naviers equations of elasticity, Computer Sciences 77.09R, Chalmers University of Technology, Göteborg, Sweden (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gustafsson, I. A class of first order factorization methods. BIT 18, 142–156 (1978). https://doi.org/10.1007/BF01931691
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01931691