Volume 7 Number 11 (Nov. 2012)
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JSW 2012 Vol.7(11): 2400-2404 ISSN: 1796-217X
doi: 10.4304/jsw.7.11.2400-2404

The Self-Adaptive Multi-Splitting Parallel Methods for Non-Hermitian Positive Definite Systems

Chuan-Long Wang1, Yan-Ping Wang1, and Jin Wang2
1Taiyuan Normal University, Taiyuan 030012, P.R.C.
2Class 390614, School of Computer Science and Engineering, Beihang University, Beijing 100191, P. R. China

Abstract—We present the convergent splitting and convergent multisplitting for linear system of algebraic equations Ax = b when the coefficient matrix is a non-hermitian positive definite matrix. Furthermore, we also establish the comparison theorems of different splittings or multisplittings based on numerical radius. Mainly, we propose two new selfadaptive multisplitting parallel methods which the weighting matrices are self-adaptive. Finally, we give an application to solve the two- dimensional advection-diffusion equations.

Index Terms—Non-hermitian matrix, positive definite matrix, multisplitting, comparison theorem


Cite: Chuan-Long Wang, Yan-Ping Wang,and Jin Wang "The Self-Adaptive Multi-Splitting Parallel Methods for Non-Hermitian Positive Definite Systems," Journal of Software vol. 7, no. 11, pp. 2400-2404, 2012.

General Information

ISSN: 1796-217X (Online)
Frequency:  Bimonthly (Since 2020)
Editor-in-Chief: Prof. Antanas Verikas
Executive Editor: Ms. Yoyo Y. Zhou
Abstracting/ Indexing: DBLP, EBSCO, Google Scholar, ProQuest, INSPEC(IET), ULRICH's Periodicals Directory, WorldCat, etc
E-mail: jsw@iap.org
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