A class of triangular splitting methods for saddle point problems

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• 作者：Qing-Qing Zheng^a ; ^b ; Chang-Feng Ma^a ; ^{macf@fjnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65F10 ; 65F50
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：298
• 期：Complete
• 页码：13-23
• 全文大小：523 K

文摘

In this paper, we study a class of efficient iterative algorithms for the large sparse nonsingular saddle point problems based on the upper and lower triangular (ULT) splitting of the coefficient matrix. We call these algorithms ULT methods. First, the ULT algorithm is established and the characteristic of eigenvalues of the iteration matrix of these new methods is analyzed. Then we give the sufficient and necessary conditions for the convergence of these ULT methods. Moreover, the optimal iteration parameters and the corresponding convergence factors for some special cases of the ULT methods are presented. Numerical experiments on a few model problems are presented to support the theoretical results and examine the numerical effectiveness of these new methods.