Non-stationary iterative solution of positive definite linear systems

Abstract

A semi-iterative method (RFII-SI method) related to the Richardson's second degree iterative method (RFII method) is developed. Both methods are applied to the class of positive definite algebraic linear systems, which includes the Ortega and the stochastic problems. Their convergence is studied through a theoretical point of view, meanwhile computational results of these methods and those of the non-stationary first degree Richardson method (NSR) are shown for comparison. The analysis is applicable to every positive definite linear problem whose matrix possesses two clusters of eigenvalues.

Keywords:

• Non-stationary method
• semiiterative method
• Chebyshev extrapolation
• Ortega problem
• stochastic problem

C.R. Category:

• G.1.3