Positive Definite and Semi-Definite Splitting Methods for Non-Hermitian Positive Definite Linear Systems
Year: 2016
Author: Na Huang, Changfeng Ma
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 300–316
Abstract
In this paper, we further generalize the technique for constructing the normal (or positive definite) and skew-Hermitian splitting iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting (PPS) methods, and prove that the sequence produced by the PPS method converges unconditionally to the unique solution of the system. Moreover, we propose two kinds of typical practical choices of the PPS method and study the upper bound of the spectral radius of the iteration matrix. In addition, we show the optimal parameters such that the spectral radius achieves the minimum under certain conditions. Finally, some numerical examples are given to demonstrate the effectiveness of the considered methods.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1511-m2015-0299
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 300–316
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Linear systems Splitting method Non-Hermitian matrix Positive definite matrix Positive semi-definite matrix Convergence analysis.
Author Details
Na Huang Email
Changfeng Ma Email
-
Second-order IMEX scheme for a system of partial integro-differential equations from Asian option pricing under regime-switching jump-diffusion models
Chen, Yong
Numerical Algorithms, Vol. 89 (2022), Iss. 4 P.1823
https://doi.org/10.1007/s11075-021-01174-x [Citations: 7] -
The Uzawa-PPS iteration methods for nonsingular and singular non-Hermitian saddle point problems
Li, Cheng-Liang | Ma, Chang-FengComputers & Mathematics with Applications, Vol. 75 (2018), Iss. 2 P.703
https://doi.org/10.1016/j.camwa.2017.10.003 [Citations: 5] -
The PPS method-based constraint preconditioners for generalized saddle point problems
Shen, Hai-Long | Wu, Hong-Yu | Shao, Xin-Hui | Song, Xiao-DiComputational and Applied Mathematics, Vol. 38 (2019), Iss. 1
https://doi.org/10.1007/s40314-019-0792-x [Citations: 5] -
An Uzawa-DOS method for solving saddle-point problems
Ebadi, Ghodrat | Mehrabi, Khosro | Stanimirović, Predrag S.Numerical Algorithms, Vol. (2024), Iss.
https://doi.org/10.1007/s11075-024-01873-1 [Citations: 0] -
Second-order convergent IMEX scheme for integro-differential equations with delays arising in option pricing under hard-to-borrow jump-diffusion models
Chen, Yong
Computational and Applied Mathematics, Vol. 41 (2022), Iss. 2
https://doi.org/10.1007/s40314-022-01783-9 [Citations: 1]