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Volume 24, Issue 4
A Shift-Splitting Preconditioner for Non-Hermitian Positive Definite Matrices

Zhong-zhi Bai, Jun-feng Yin & Yang-feng Su

J. Comp. Math., 24 (2006), pp. 539-552.

Published online: 2006-08

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  • Abstract

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.

  • Keywords

Non-Hermitian positive definite matrix, Matrix splitting, Preconditioning, Krylov subspace method, Convergence.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JCM-24-539, author = {Zhong-zhi Bai, Jun-feng Yin and Yang-feng Su}, title = {A Shift-Splitting Preconditioner for Non-Hermitian Positive Definite Matrices}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {4}, pages = {539--552}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8773.html} }
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 -

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.

Zhong-zhi Bai, Jun-feng Yin and Yang-feng Su. (2006). A Shift-Splitting Preconditioner for Non-Hermitian Positive Definite Matrices. Journal of Computational Mathematics. 24 (4). 539-552. doi:
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