ML(n)BiCGStab: Reformulation, Analysis and Implementation

Man-Chung Yeung

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arXiv · 1011.5314

ML(n)BiCGStab: Reformulation, Analysis and Implementation

Man-Chung Yeung

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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.

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BibTeX RIS

Man-Chung Yeung. 2010-11-24. ML(n)BiCGStab: Reformulation, Analysis and Implementation. https://arxiv.org/abs/1011.5314

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