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 restrictively preconditioned conjugate gradient （RPCG） method is further developed to solve large sparse system of linear equations of a block two-by-two structure. The basic idea of this new approach is that we...The restrictively preconditioned conjugate gradient （RPCG） method is further developed to solve large sparse system of linear equations of a block two-by-two structure. The basic idea of this new approach is that we apply the RPCG method to the normal-residual equation of the block two-by-two linear system and construct each required approximate matrix by making use of the incomplete orthogonal factorization of the involved matrix blocks. Numerical experiments show that the new method, called the restrictively preconditioned conjugate gradient on normal residual （RPCGNR）, is more robust and effective than either the known RPCG method or the standard conjugate gradient on normal residual （CGNR） method when being used for solving the large sparse saddle point problems.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supported by the National Basic Research Program (No.2005CB321702)the China NNSF Outstanding Young Scientist Foundation (No.10525102)the National Natural Science Foundation (No.10471146),P.R.China
文摘The restrictively preconditioned conjugate gradient （RPCG） method is further developed to solve large sparse system of linear equations of a block two-by-two structure. The basic idea of this new approach is that we apply the RPCG method to the normal-residual equation of the block two-by-two linear system and construct each required approximate matrix by making use of the incomplete orthogonal factorization of the involved matrix blocks. Numerical experiments show that the new method, called the restrictively preconditioned conjugate gradient on normal residual （RPCGNR）, is more robust and effective than either the known RPCG method or the standard conjugate gradient on normal residual （CGNR） method when being used for solving the large sparse saddle point problems.
