共查询到20条相似文献,搜索用时 45 毫秒
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In this paper, we present a new preconditioned AOR-type iterative method for solving the linear system Ax=b, where A is a Z-matrix, and prove its convergence. Then we give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method. Finally, we give two numerical examples to illustrate our results. 相似文献
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In this paper, we present some comparison theorems on preconditioned iterative method for solving Z-matrices linear systems, Comparison results show that the rate of convergence of the Gauss–Seidel-type method is faster than the rate of convergence of the SOR-type iterative method. 相似文献
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《Applied Mathematics Letters》2001,14(5):625-630
Linear systems of the form Ax = b, where the matrix A is symmetric and positive definite, often arise from the discretization of elliptic partial differential equations. A very successful method for solving these linear systems is the preconditioned conjugate gradient method. In this paper, we study parallel preconditioners for the conjugate gradient method based on the block two-stage iterative methods. Sufficient conditions for the validity of these preconditioners are given. Computational results of these preconditioned conjugate gradient methods on two parallel computing systems are presented. 相似文献
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《Journal of Computational and Applied Mathematics》1997,83(1):115-118
In this paper, we consider a preconditioned iterative method for solving the linear system Ax = b, which is a generalization of a method proposed in Kotakemori et al. [3] and prove its convergence for the case when A is an H-matrix. 相似文献
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Recently, Bai et al. (2013) proposed an effective and efficient matrix splitting iterative method, called preconditioned modified Hermitian/skew-Hermitian splitting (PMHSS) iteration method, for two-by-two block linear systems of equations. The eigenvalue distribution of the iterative matrix suggests that the splitting matrix could be advantageously used as a preconditioner. In this study, the CGNR method is utilized for solving the PMHSS preconditioned linear systems, and the performance of the method is considered by estimating the condition number of the normal equations. Furthermore, the proposed method is compared with other PMHSS preconditioned Krylov subspace methods by solving linear systems arising in complex partial differential equations and a distributed control problem. The numerical results demonstrate the difference in the performance of the methods under consideration. 相似文献
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Preconditioned GSOR iterative method for a class of complex symmetric system of linear equations 下载免费PDF全文
Davod Hezari Vahid Edalatpour Davod Khojasteh Salkuyeh 《Numerical Linear Algebra with Applications》2015,22(4):761-776
In this paper, we present a preconditioned variant of the generalized successive overrelaxation (GSOR) iterative method for solving a broad class of complex symmetric linear systems. We study conditions under which the spectral radius of the iteration matrix of the preconditioned GSOR method is smaller than that of the GSOR method and determine the optimal values of iteration parameters. Numerical experiments are given to verify the validity of the presented theoretical results and the effectiveness of the preconditioned GSOR method. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Based on the preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration method, we introduce a lopsided PMHSS (LPMHSS) iteration method for solving a broad class of complex symmetric linear systems. The convergence properties of the LPMHSS method are analyzed, which show that, under a loose restriction on parameter α, the iterative sequence produced by LPMHSS method is convergent to the unique solution of the linear system for any initial guess. Furthermore, we derive an upper bound for the spectral radius of the LPMHSS iteration matrix, and the quasi-optimal parameter α ? which minimizes the above upper bound is also obtained. Both theoretical and numerical results indicate that the LPMHSS method outperforms the PMHSS method when the real part of the coefficient matrix is dominant. 相似文献
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《Journal of Computational and Applied Mathematics》1998,100(1):1-9
Many papers have discussed preconditioned block iterative methods for solving full rank least-squares problems. However very few papers studied iterative methods for solving rank-deficient least-squares problems. Miller and Neumann (1987) proposed the 4-block SOR method for solving the rank-deficient problem. Here a 2-block SOR method and a 3-block SOR method are proposed to solve such problem. The convergence of the block SOR methods is studied. The optimal parameters are determined. Comparison between the 2-block SOR method and the 3-block SOR method is given also. 相似文献
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S. Bocanegra F. F. Campos A. R. L. Oliveira 《Computational Optimization and Applications》2007,36(2-3):149-164
We devise a hybrid approach for solving linear systems arising from interior point methods applied to linear programming problems. These systems are solved by preconditioned conjugate gradient method that works in two phases. During phase I it uses a kind of incomplete Cholesky preconditioner such that fill-in can be controlled in terms of available memory. As the optimal solution of the problem is approached, the linear systems becomes highly ill-conditioned and the method changes to phase II. In this phase a preconditioner based on the LU factorization is found to work better near a solution of the LP problem. The numerical experiments reveal that the iterative hybrid approach works better than Cholesky factorization on some classes of large-scale problems. 相似文献
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Numerical Algorithms - In practical computations, the (preconditioned) conjugate gradient (P)CG method is the iterative method of choice for solving systems of linear algebraic equations Ax = b... 相似文献
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陈蔚 《数学物理学报(A辑)》2001,21(2):201-210
考虑数值求解具有对流项的高维拟线性Sobolev方程,构造了特征有限元格式,提出用交替方向预处理迭代法求特征有限元格式在每一时间步所产生的代数方程组的近似解,整个计算过程仅对一个可方向交替的预处理矩阵求逆一次,大大降低了计算量.证明了迭代解的最佳L^2模误差估计,并给出了算法的拟优工作量估计. 相似文献
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We derive a fourth-order compact finite difference scheme for a two-dimensional elliptic problem with a mixed derivative and constant coefficients. We conduct experimental study on numerical solution of the problem discretized by the present compact scheme and the traditional second-order central difference scheme. We study the computed accuracy achieved by each scheme and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from the difference schemes. 相似文献
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E. Ovtchinnikov 《Linear algebra and its applications》2006,415(1):140-166
The paper presents convergence estimates for a class of iterative methods for solving partial generalized symmetric eigenvalue problems whereby a sequence of subspaces containing approximations to eigenvectors is generated by combining the Rayleigh-Ritz and the preconditioned steepest descent/ascent methods. The paper uses a novel approach of studying the convergence of groups of eigenvalues, rather than individual ones, to obtain new convergence estimates for this class of methods that are cluster robust, i.e. do not involve distances between computed eigenvalues. 相似文献
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Complex valued systems of equations with a matrix R + 1S where R and S are real valued arise in many applications. A preconditioned iterative solution method is presented when R and S are symmetric positive semi‐definite and at least one of R, S is positive definite. The condition number of the preconditioned matrix is bounded above by 2, so only very few iterations are required. Applications when solving matrix polynomial equation systems, linear systems of ordinary differential equations, and using time‐stepping integration schemes based on Padé approximation for parabolic and hyperbolic problems are also discussed. Numerical comparisons show that the proposed real valued method is much faster than the iterative complex symmetric QMR method. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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Projection methods have emerged as competitive techniques for solving large scale matrix Lyapunov equations. We explore the numerical solution of this class of linear matrix equations when a Minimal Residual (MR) condition is used during the projection step. We derive both a new direct method, and a preconditioned operator-oriented iterative solver based on CGLS, for solving the projected reduced least squares problem. Numerical experiments with benchmark problems show the effectiveness of an MR approach over a Galerkin procedure using the same approximation space. 相似文献
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刘兴平 《应用数学与计算数学学报》1995,9(2):60-67
预条件广义共轭余量法并行和向量计算的关键是预条件计算是否可并行和向量计算,我们利用分而治之的原则,构造了一处块预条件矩阵M,这里的矩阵M是通过对线性代数方程组Ax=f的矩阵A进行块分解,在块分解中利用近似逆技术。这样分解形成的预条件矩阵M在迭代计算时,可向量或并行计算。 相似文献