Left conjugate gradient method for non‐Hermitian linear systems
Liping Wang, Yu-Hong Dai · Numerical Linear Algebra with Applications · 2008
Abstract 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.