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Stone’s original and symmetric factorization procedure : contrasts and comparisons Kusiak, Robert A.

Abstract

The numerical solution of elliptic boundary value problems on rectangular regions with Dirichlet boundary conditions is considered. The well-known finite difference scheme is used to discretize the continuous problem. The solution is now expressed as the unknown vector in a high order matrix equation. In general, efficient direct methods for obtaining the solution of the matrix equation are not known. There are several well-known iteration schemes commonly used to solve such problems. The main disadvantage of these methods is that the number of computations which are required to solve the matrix equation increases in a nonlinear way with the number of equations to be solved. Stone's original and symmetric strongly implicit factorization procedure are considered. The known results concerning the convergence properties of each iteration are presented. A new result concerning the symmetric factorization is presented and the results of numerical investigations are presented.

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