Higher Order Aitken Extrapolation with Application to Converging and Diverging Gauss-Seidel Iterations

@article{Tiruneh2013HigherOA,
title={Higher Order Aitken Extrapolation with Application to Converging and Diverging Gauss-Seidel Iterations},
author={A. T. Tiruneh},
journal={ArXiv},
year={2013},
volume={abs/1310.4288}
}

In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition of high Eigen values of the iteration matrix to enable convergence. While extrapolation of a convergent fixed point iteration using a geometric series sum is a known form of Aitken acceleration, it is shown that in this paper, the same formula… Expand