ML(n)BiCGStab: Reformulation, Analysis and Implementation
Abstract
With the aid of index functions, we re-derive the ML(n)BiCGStab algorithm in a paper by Yeung and Chan in 1999 in a more systematic way. It turns out that there are n ways to define the ML(n)BiCGStab residual vector. Each definition will lead to a different ML(n)BiCGStab algorithm. We demonstrate this by presenting a second algorithm which requires less storage. In theory, this second algorithm serves as a bridge that connects the Lanczos-based BiCGStab and the Arnoldi-based FOM while ML(n)BiCG a bridge connecting BiCG and FOM. We also analyze the breakdown situations from the probabilistic point of view and summarize some useful properties of ML(n)BiCGStab. Implementation issues are also addressed.
Cite
@article{arxiv.1011.5314,
title = {ML(n)BiCGStab: Reformulation, Analysis and Implementation},
author = {Man-Chung Yeung},
journal= {arXiv preprint arXiv:1011.5314},
year = {2010}
}
Comments
This paper is dedicated to the memory of Prof. Gene Golub. Most part of the paper was presented in Gene Golub Memorial Conference, Feb. 29-Mar. 1, 2008, University of Massachusetts, Dartmouth, U.S.A