Derivation of BiCG from the Conditions Defining Lanczos' Method for Solving a System of Linear Equations

0404018 - UIVT-O 20000155 RIV CZ eng J - Journal Article
Tichý, Petr - Zítko, Jan
Derivation of BiCG from the Conditions Defining Lanczos' Method for Solving a System of Linear Equations.
Applications of Mathematics. Roč. 43, č. 5 (1998), s. 381-388. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA ČR GA201/96/0918
Institutional research plan: AV0Z1030915
Keywords : biorthogonalization * linear equations * biconjugate gradient method
Subject RIV: BA - General Mathematics
http://dml.cz/handle/10338.dmlcz/134394

Lanczos' method for solving the system of linear algebraic equations Ax=b consists in constructing a sequence of approximations to the solution and corresponding residual vectors which are orthogonal to certain Krylov subspace. These sequences of vectors can be computed by the BiCG (BiOMin) algorithm. We will shov how to obtain recurrences of BiCG (BiOMin) directly from the orthogonal conditions.
Permanent Link: http://hdl.handle.net/11104/0124299