Derivation of BiCG from the conditions defining lanczos' method for solving a system of linear equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Derivation of BiCG from the conditions defining lanczos' method for solving a system of linear equations

Authors:	Petr Tichý Jan Zítko

Affiliation:	(1) Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University of Prague, Malostranské, námstí 25, 11800 Praha 1, Czech Republic

Abstract:	Lanczos' method for solving the system of linear algebraic equations Ax=b consists in constructing a sequence of vectors x_k in such a way that $r_k = b - Ax_k in ;;r_0 + Amathcal{K}_k (A,r_0 )$ and $r_k bot mathcal{K}_k (A^T ,tilde r_0 )$ . This sequence of vectors can be computed by the BiCG (BiOMin) algorithm. In this paper is shown how to obtain the recurrences of BiCG (BiOMin) directly from this conditions.

Keywords:	biorthogonalization linear equations biconjugate gradient method
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