ABSTRACT

Based on the non-alternating preconditioned HSS iteration scheme, a class of the Uzawa-NPHSS iteration method for solving nonsingular and singular non-Hermitian saddle point problems with the (1,1) part of the coefficient matrix being non-Hermitian positive definite is established. The convergence properties for the nonsingular saddle point problems and the semi-convergence properties for the singular ones of the proposed method are carefully discussed under suitable conditions. Meanwhile, the distribution of eigenvalues and the forms of the eigenvectors of the preconditioned matrix are analysed in detail. Additionally, the parameter selection strategy for the Uzawa-NPHSS iteration method is provided. Numerical experiments are implemented to confirm the theoretical results, which show the feasibility and effectiveness of the proposed method.

摘要

基于非交替预条件HSS迭代方案，一类求解系数矩阵(1,1)部分为非厄米正定的非奇异和奇异非厄米鞍点问题的Uzawa-NPHSS迭代方法为已确立的。在合适的条件下，对所提方法的非奇异鞍点问题的收敛性质和奇异问题的半收敛性质进行了仔细讨论。同时，详细分析了预处理矩阵的特征值分布和特征向量的形式。此外，还提供了 Uzawa-NPHSS 迭代方法的参数选择策略。通过数值实验验证了理论结果，表明了所提方法的可行性和有效性。