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
The generalized least squares (LS) problem ... (Ax - b)[sup TW[sup -1](Ax - b) appears in, many application areas. Here W is an m × m symmetric positive definite matrix and A is an m × n matrix with m ≥ n. ...The generalized least squares (LS) problem ... (Ax - b)[sup TW[sup -1](Ax - b) appears in, many application areas. Here W is an m × m symmetric positive definite matrix and A is an m × n matrix with m ≥ n. Since the problem has many solutions in rank deficient case, some special preconditioned techniques are adapted to obtain the minimum 2-norm solution. A block SOR method and the preconditioned conjugate gradient (PCG) method are proposed here. Convergence and optimal relaxation parameter for the block SOR method are studied. An error bound for the PCG method is given. The comparison of these methods is investigated. Some remarks on the implementation of the methods and the operation cost are given as well. [ABSTRACT FROM AUTHOR]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。
基金CNPq, Brazil!301035/93-8University of Macao!RG010/ 99- 00S / JXQ / FST
文摘The generalized least squares (LS) problem ... (Ax - b)[sup TW[sup -1](Ax - b) appears in, many application areas. Here W is an m × m symmetric positive definite matrix and A is an m × n matrix with m ≥ n. Since the problem has many solutions in rank deficient case, some special preconditioned techniques are adapted to obtain the minimum 2-norm solution. A block SOR method and the preconditioned conjugate gradient (PCG) method are proposed here. Convergence and optimal relaxation parameter for the block SOR method are studied. An error bound for the PCG method is given. The comparison of these methods is investigated. Some remarks on the implementation of the methods and the operation cost are given as well. [ABSTRACT FROM AUTHOR]
