Structure of the polynomials in preconditioned BiCG algorithms and the switching direction of preconditioned systems
Numerical Analysis
2020-01-27 v3 Numerical Analysis
Abstract
We present a theorem that defines the direction of a preconditioned system for the bi-conjugate gradient (BiCG) method, and we extend it to preconditioned bi-Lanczos-type algorithms. We show that the direction of a preconditioned system is switched by construction and by the settings of the initial shadow residual vector. We analyze and compare the polynomial structures of four preconditioned BiCG algorithms.
Keywords
Cite
@article{arxiv.1603.00175,
title = {Structure of the polynomials in preconditioned BiCG algorithms and the switching direction of preconditioned systems},
author = {Shoji Itoh and Masaaki Sugihara},
journal= {arXiv preprint arXiv:1603.00175},
year = {2020}
}