Optimum sor methods for a class of linear systems

Abstract

For a class of linear systems Ax = b, with A block tridiagonal of a special form, it is proved first that the optimum SOR method associated with Ais much faster than even the fastest optimum second order stationary method of Manteuffel and therefore the most efficient one to use for their solution. Next, in case A is of a more special type, explicit expressions for the eigenvalues of the point and block Jacobi matrices are found and then the optimum parameters of the corresponding SOR methods are determined by means of the algorithm by Young and Eidson. Finally the theory developed is applied for the solution of the resulting linear systems from the discretization by 5-point formulas of one parabolic and one elliptic PDE's when boundary value techniques are used.

Keywords:

• Successive Overrelaxation (SOR) Methods
• Stationary Second Order Manteuffer's Method
• Numerical Solution Of Pde's By Boundary Value Techniques

C.R. Categories:

• 5.14
• 5.17