3×3块鞍点问题作为一类特殊的线性方程组,其迭代方法的研究极具挑战性。基于经典的广义逐次超松弛(Generalized Successive Over Relaxation,GSOR)方法,针对3×3块大型稀疏鞍点问题,提出了三参数的中心预处理GSOR方法并讨论了...3×3块鞍点问题作为一类特殊的线性方程组,其迭代方法的研究极具挑战性。基于经典的广义逐次超松弛(Generalized Successive Over Relaxation,GSOR)方法,针对3×3块大型稀疏鞍点问题,提出了三参数的中心预处理GSOR方法并讨论了其收敛性。同时,通过数值实验验证了新方法在计算花费方面优于中心预处理的Uzawa-Low方法。进一步地,还将新方法拓展到i×i块鞍点问题,提出了相应的GSOR类迭代框架,通过数值实验和数据分析,给出了选择较优i的初步建议。展开更多
We consider here iterative methods for the generalized least squares problem defined as min(Ax-b)TW-1 (Ax-b) with W symmetric and positive definite. We develop preconditioned SOR methods specially devised also for the...We consider here iterative methods for the generalized least squares problem defined as min(Ax-b)TW-1 (Ax-b) with W symmetric and positive definite. We develop preconditioned SOR methods specially devised also for the augmented systems of the problem. We establish the convergence region for the relaxation parameter and discuss, for one of the resulting SOR methods, the optimal value of this parameter. The convergence analysis and numerical experiments show that the preconditioned block SOR methods are very good alternatives for solving the problem.展开更多
文摘3×3块鞍点问题作为一类特殊的线性方程组,其迭代方法的研究极具挑战性。基于经典的广义逐次超松弛(Generalized Successive Over Relaxation,GSOR)方法,针对3×3块大型稀疏鞍点问题,提出了三参数的中心预处理GSOR方法并讨论了其收敛性。同时,通过数值实验验证了新方法在计算花费方面优于中心预处理的Uzawa-Low方法。进一步地,还将新方法拓展到i×i块鞍点问题,提出了相应的GSOR类迭代框架,通过数值实验和数据分析,给出了选择较优i的初步建议。
文摘We consider here iterative methods for the generalized least squares problem defined as min(Ax-b)TW-1 (Ax-b) with W symmetric and positive definite. We develop preconditioned SOR methods specially devised also for the augmented systems of the problem. We establish the convergence region for the relaxation parameter and discuss, for one of the resulting SOR methods, the optimal value of this parameter. The convergence analysis and numerical experiments show that the preconditioned block SOR methods are very good alternatives for solving the problem.
