Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations
- 1 September 1968
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 5 (3) , 530-558
- https://doi.org/10.1137/0705044
Abstract
Summary:The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values of the parameters successfully without a deeper a priori analysis of the linear system solvedKeywords
This publication has 7 references indexed in Scilit:
- An Approximate Factorization Procedure for Solving Self-Adjoint Elliptic Difference EquationsSIAM Journal on Numerical Analysis, 1968
- An extrapolation procedure for solving linear systemsQuarterly of Applied Mathematics, 1962
- On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit MethodsJournal of the Society for Industrial and Applied Mathematics, 1955
- The Numerical Solution of Parabolic and Elliptic Differential EquationsJournal of the Society for Industrial and Applied Mathematics, 1955
- Convergence Rates of Iterative Treatments of Partial Differential EquationsMathematical Tables and Other Aids to Computation, 1950
- IX. The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry damPhilosophical Transactions of the Royal Society A, 1911
- Ueber eine neue Auflösungsart der bei der Methode der kleinsten Quadrate vorkommenden lineären GleichungenAstronomische Nachrichten, 1845