ASSESSMENT OF SOME ACCELERATION SCHEMES IN THE SOLUTION OF SYSTEMS OF LINEAR EQUATIONS

Abstract

An assessment of acceleration schemes in the solution of systems of linear equations has been studied. The iterative methods:Jacobi, Gauss-Seidel and SOR methods were incorporated into the acceleration scheme (Chebyshev extrapolation, Residual smoothing, Accelerated gradient and Richardson Extrapolation)to speed up their convergence. The Conjugate gradient methods of GMRES,BICGSTAB and QMR were also assessed. The research focused on Banded systems, Tridiagonal systems and Dense Symmetric positive definite systems of linear equations for numerical experiments. The experiments were based on the following performance criteria: convergence, number of iterations, speed of convergence and relative residual of each method. Matlab version 7.0.1 was used for the computation of the resulting algorithms. Assessment of the numerical results showed that the accelerated schemes improved the performance of Jacobi, Gauss-Seidel and SOR methods. The Chebyshev and Richardson acceleration methods converged faster than the conjugate gradient methods of GMRES, MINRES, QMR and BICGSTAB in general.