Optimal block accelerated overrelaxation method for a large class of 2-cyclic matrices

Abstract

The problem of exactly determining the optimal pair of parameters for the block Accelerated Overrelaxation (AOR) method, when it applies to large linear systems with a 2-cyclic coefficient matrix, is considered. Under certain hypotheses, concerning the eigenvalues of the associated block Jacobi iteration matrix, explicit expressions of the optimal parameters and their corresponding spectral radius are obtained. These results extend, and correct, the literature on such applications.

Keywords:

• Iterative methods
• accelerated overrelaxation method
• 2-cyclic matrices
• extrapolation
• eigenvalues
• spectral radius

SUBJECT CLASSIFICATIONS. AMS(M0S):

• 65F10
• 65F15
• CR:G.1.3