Premium
Left conjugate gradient method for non‐Hermitian linear systems
Author(s) -
Wang LiPing,
Dai YuHong
Publication year - 2008
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.600
Subject(s) - conjugate gradient method , hermitian matrix , conjugate , mathematics , derivation of the conjugate gradient method , block (permutation group theory) , complex conjugate , conjugate residual method , linear system , nonlinear conjugate gradient method , algorithm , mathematical analysis , pure mathematics , computer science , combinatorics , gradient descent , artificial intelligence , artificial neural network
Recently, Yuan et al . ( BIT : Numer. Math. 2004; 44 (1):189–207) proposed the left conjugate gradient (LCG) method for real positive‐definite linear systems. This paper aims to generalize their method for solving complex non‐Hermitian linear systems. To avoid the breakdown that possibly occurred in the LCG method, we also propose the block left conjugate direction method and the block LCG (BLCG) method. It is found that no breakdown occurs in the BLCG method and the block idea also applies to the real nonsymmetric case. Numerical experiments demonstrate the usefulness of the proposed LCG method. Copyright © 2008 John Wiley & Sons, Ltd.