TY - JOUR
T1 - A Shift-Splitting Preconditioner for Non-Hermitian Positive Definite Matrices
AU - Zhong-zhi Bai, Jun-feng Yin & Yang-feng Su
JO - Journal of Computational Mathematics
VL - 4
SP - 539
EP - 552
PY - 2006
DA - 2006/08
SN - 24
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8773.html
KW - Non-Hermitian positive definite matrix, Matrix splitting, Preconditioning, Krylov subspace method, Convergence.
AB - <p style="text-align: justify;">A shift splitting concept is introduced and, correspondingly, a shift-splitting iteration scheme and a shift-splitting preconditioner are presented, for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned non-Hermitian positive definite matrix. The convergence property of the shift-splitting iteration method and the eigenvalue distribution of the shift-splitting preconditioned matrix are discussed in depth, and the best possible choice of the shift is investigated in detail. Numerical computations show that the shift-splitting preconditioner can induce accurate, robust and effective preconditioned Krylov subspace iteration methods for solving the large sparse non-Hermitian positive definite systems of linear equations.</p>