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给出了解线性方程组Ax=b的一个新的预条件因子P．应用Gauss—Seidel迭代格式于预条件线性方程组PAx=Pb,并证明了当矩阵A为H-矩阵时,此预条件Gauss—Seidel方法是收敛的．最后,数值算例说明文中所给预条件Gauss—Seidel方法是有效的． 相似文献
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江跃勇 《绵阳师范学院学报》2007,26(11):10-14
J.H.Yun提出了一种新的计算块三对角M矩阵预条件的算法,这种方法具有天然的并行性,解决了ILU分解不易并行化的缺点,能有效节约计算时间。以对称M矩阵作为例子,将以上方法推广到一般的对称M矩阵,使得在构造这一类矩阵的不完全分解预条件方法时,能够更加快速有效。关于预条件子的定理及其证明将会被给出。最后,数值实验将会被用来验证我们的定理结论。 相似文献
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Chan和Bertaccini等提出使用循环矩阵作为预条件矩阵的GMRES方法来求解由边值法(BVM)离散常微分方程初值问题的线性系统是优于GMRES方法的.本文基于广义Admas法(GAMs)离散常微分方程初值问题的线性系统中矩阵的双对角形式,提出了一类新的循环预条件矩阵来加速GMRES的收敛性,并且从理论上证明了方法的收敛性,数值实验表明了这种方法的有效性. 相似文献
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白中治 《上海大学学报(英文版)》2004,8(4)
For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices.Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices for some typical matrices from the real-world applications. 相似文献
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ＯＲＴＨＯＧＯＮＡＬ ＰＲＯＪＥＣｌｌＯＮ ＯＦＴＨＥ ＤＯＭＡＩＮＢＯＲＮＤＡＲＹＯＰＥＲＡＴＯＲＦＯＲＥＬＬＩＰＩＴＩＣＰＲＯＢＬＥＭＢＹＤＯＭＡＩＮＤＥＣＯＭＰＬＳＩＴＩＯＮ（石佩虎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｎｉａｔｉｃｓａｎｄＭｅｃ?.. 相似文献
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对于广义鞍点问题,基于参数化的Uzawa方法提出了一种新的预处理子,通过分析预处理后的系统,发现当参数t→0时,其特征值将集中到0和1,因此,当在Krylov子空间中使用某些GMRES迭代方法时,它将保证较好的收敛性.最后,运用Navier-Stokes方程中的一些例子进行实验,验证了这个预处理子的实际效果. 相似文献
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Vahid Esfahanian 《Journal of The Franklin Institute》2011,348(7):1208-1230
A locally power-law preconditioning algorithm is developed. This is applied to compute incompressible inviscid, steady-state, non-cavitating and cavitating flows. The preconditioning parameters are adapted automatically from the pressure of computational domain. This method suggests better convergence rates rather than the standard artificial compressibility and the standard preconditioning method. Single-fluid Euler equations, cast in their conservative form, along with the barotropic cavitation model are employed. The cell-centred Jameson's finite volume discretization technique is used to solve the preconditioned governing equations. The stabilization is achieved via the second and fourth, order artificial dissipation scheme. Explicit four-stage Runge-Kutta time integration is applied to find the steady-state condition. In this paper, the method is assessed through simulations of incompressible inviscid, steady-state, non-cavitating and cavitating flows over a 2D NACA0012 and a 2D NACA66(MOD)+a=0.8 hydrofoil section. The results show satisfactory agreement with others numerical and experimental works in pressure distribution and hydrodynamic forces. Using the power-law preconditioner decreases the convergence rate significantly. In addition, information such as the effects of the new locally power-law preconditioner, the effects of the artificial dissipation terms, and the effects of the artificial compressibility parameter, on convergence speed and solution accuracy is highlighted. 相似文献
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Construction and Analysis of Structured Preconditioners for Block Two-by-Two Matrices 总被引：3，自引：0，他引：3
白中治 《上海大学学报(英文版)》2004,8(4):397-405
For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured precondi-tioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modi-fied block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describetheir concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices.Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRESand restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with blocktwo-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices forsome typical matrices from the real-world applications. 相似文献
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薛炜 《佳木斯教育学院学报》2015,(1)
本文利用一种新的预条件矩阵讨论了预条件AOR迭代方法的收敛性,并分析了参数α、β和γ的选取对收敛速度的影响,并在讨论其收敛性的基础上加以应用。 相似文献
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