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1.
Apostolos Hadjidimos Theodore S. Papatheodorou Yiannis G. Saridikis 《Linear algebra and its applications》1983
The problem of determining fast iterative solutions of certain large, sparse, and nonsymmetric linear systems, arising in applications, is addressed here. Several iterative schemes, from the accelerated overrelaxation family, are considered. Different geometrical algorithms are used for the explicit determination of the optimal factors. Direct comparisons of the spectral radii of the resulting optimal schemes reveal that the optimal extrapolated accelerated Gauss-Seidel (EAGS) is always asymptotically faster than the optimal successive overrelaxation, while the optimal EAGS and extrapolated Gauss-Seidel strongly compete. Application of the collocation method on simple boundary-value problems is used to demonstrate our results numerically. 相似文献
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周如海 《高等学校计算数学学报(英文版)》1993,(2)
In order to solve linear interval equations Ax=b. the interval Gauss-Seidel iteration is applied to a modified equations A'x = b', where A' is obtained by eliminating all elements in the first upper codiagonal part of A. It is shown that this modified Gauss-Seidel iteration converges when the usual Gauss-Seidel iteration converges, and the modified Gauss-Seidel iteration always has a smaller convergence factor. The converse is not true. It is also pointed out that the modified Gauss-Seidel iteration can obtain a belter result comparing with the usual Gauss-Seidel iteration in some cases. Several examples confirmed these conclusions. 相似文献
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ASYNCHRONOUSMULTISPLITTINGNONLINEARGAUSS-SEIDELTYPEMETHOD¥BAIZHONGZHIANDWANGDERENAbstract:Inthispaper,weproposeaparallelGauss... 相似文献
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We consider the minimization problem with strictly convex, possibly nondifferentiable, separable cost and linear constraints.
The dual of this problem is an unconstrained minimization problem with differentiable cost which is well suited for solution
by parallel methods based on Gauss-Seidel relaxation. We show that these methods yield the optimal primal solution and, under
additional assumptions, an optimal dual solution. To do this it is necessary to extend the classical Gauss-Seidel convergence
results because the dual cost may not be strictly convex, and may have unbounded level sets.
Work supported by the National Science Foundation under grant NSF-ECS-3217668. 相似文献
6.
Chun-jiaBi Li-kangLi 《计算数学(英文版)》2004,22(1):123-136
The purpose of this paper is to study the cascadic multigrid method for the secondorder elliptic problems with curved boundary in two-dimension which are discretized by the isoparametric finite element method with numerical integration. We show that the CCG method is accurate with optimal complexity and traditional multigrid smoother (likesymmetric Gauss-Seidel, SSOR or damped Jacobi iteration) is accurate with suboptimal complexity. 相似文献
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R. Baker Kearfott 《Journal of Global Optimization》1992,2(3):259-280
In this paper, we propose modifications to a prototypical branch and bound algorithm for nonlinear optimization so that the algorithm efficiently handles constrained problems with constant bound constraints. The modifications involve treating subregions of the boundary identically to interior regions during the branch and bound process, but using reduced gradients for the interval Newton method. The modifications also involve preconditioners for the interval Gauss-Seidel method which are optimal in the sense that their application selectively gives a coordinate bound of minimum width, a coordinate bound whose left endpoint is as large as possible, or a coordinate bound whose right endpoint is as small as possible. We give experimental results on a selection of problems with different properties. 相似文献
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Li-Xiao Duan & Guo-Feng Zhang 《高等学校计算数学学报(英文版)》2021,14(3):714-737
The variants of randomized Kaczmarz and randomized Gauss-Seidel algorithms are two effective stochastic iterative methods for solving ridge regression
problems. For solving ordinary least squares regression problems, the greedy randomized Gauss-Seidel (GRGS) algorithm always performs better than the randomized Gauss-Seidel algorithm (RGS) when the system is overdetermined. In this paper, inspired by the greedy modification technique of the GRGS algorithm, we extend
the variant of the randomized Gauss-Seidel algorithm, obtaining a variant of greedy
randomized Gauss-Seidel (VGRGS) algorithm for solving ridge regression problems.
In addition, we propose a relaxed VGRGS algorithm and the corresponding convergence theorem is established. Numerical experiments show that our algorithms
outperform the VRK-type and the VRGS algorithms when $m > n$. 相似文献
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黎稳 《高等学校计算数学学报(英文版)》2002,11(1):89-93
In this paper we prove that the convergence rate of the modified Gauss-Seidel method is a monotonic function for some precondition parameters. 相似文献
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陈恒新 《数学的实践与认识》2002,32(1):125-131
本文证明了当线性方程组系数矩阵 A之 Jacobi迭代矩阵 B=L+ U≥ 0 ,ρ( B) <1时 Gauss-Seidel法之迭代矩阵 G=L1,1的谱半径 ρ( G) =ρ( L1,1)是 ρ( Lr,w) ( 0≤ r≤w≤ 1 ,w>0 )中的最小值 ,即此时 Gauss-Seidel迭代是 AOR法中收敛最快的迭代法 .并且对 JOR法 (谱半径为 ρ( Jw) )和 SAOR法也作了相应的论述 . 相似文献
11.
Xin-Guo Liu & Jian-Ping You 《数学研究》2015,48(1):66-78
This paper deals with numerical methods for the Maxnear criterion of multiple-sets
canonical analysis. Optimality conditions are derived. Upper and lower bounds
of the optimal objective function value are presented. Two iterative methods are proposed.
One is an alternating variable method, and the other called Gauss-Seidel method
is an inexact version of the alternating variable method. Convergence of these methods
are analyzed. A starting point strategy is suggested for both methods. Numerical
results are presented to demonstrate the efficiency of these methods and the starting
point strategy. 相似文献
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In this paper, a local multilevel algorithm is investigated for solving linear systems arising from adaptive finite element approximations of second order elliptic problems with smooth complex coefficients. It is shown that the abstract theory for local multilevel algorithm can also be applied to elliptic problems whose dominant coefficient is complex valued. Assuming that the coarsest mesh size is sufficiently small, we prove that this algorithm with Gauss-Seidel smoother is convergent and optimal on the adaptively refined meshes generated by the newest vertex bisection algorithm. Numerical experiments are reported to confirm the theoretical analysis. 相似文献
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《Mathematical and Computer Modelling》1996,23(7):29-43
A parallel variant of the block Gauss-Seidel iteration for the solution of block-banded linear systems is presented. The coefficient matrix is partitioned among the processors as in the domain decomposition methods and then it is split so that the resulting iterative method has the same spectral properties of the block Gauss-Seidel iteration.The parallel algorithm is applied to the solution of block-banded linear systems arising from the numerical discretization of initial value problems by means of Boundary Value Methods (BVMs). BVMs define a new approach for the solution of ordinary differential equations and seem to be attractive for their interesting stability properties and a possible parallel implementation. In this paper, we refer to BVMs based on the extended trapezoidal rules. 相似文献
15.
José Manuel Gutiérrez Ángel Alberto Magreñán Juan Luis Varona 《Applied mathematics and computation》2011,218(6):2467-2479
In this paper we introduce a process we have called “Gauss-Seidelization” for solving nonlinear equations. We have used this name because the process is inspired by the well-known Gauss-Seidel method to numerically solve a system of linear equations. Together with some convergence results, we present several numerical experiments in order to emphasize how the Gauss-Seidelization process influences on the dynamical behavior of an iterative method for solving nonlinear equations. 相似文献
16.
《Journal of Computational and Applied Mathematics》2005,183(2):312-326
This paper is concerned with an optimal boundary control of the cooling down process of glass, an important step in glass manufacturing. Since the computation of the complete radiative heat transfer equations is too complex for optimization purposes, we use simplified approximations of spherical harmonics including a practically relevant frequency bands model. The optimal control problem is considered as a constrained optimization problem. A first-order optimality system is derived and decoupled with the help of a gradient method based on the solution to the adjoint equations. The arising partial differential–algebraic equations of mixed parabolic–elliptic type are numerically solved by a self-adaptive method of lines approach of Rothe type. Adaptive finite elements in space and one-step methods of Rosenbrock-type with variable step sizes in time are applied. We present numerical results for a two-dimensional glass cooling problem. 相似文献
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In this paper, we apply finite element Galerkin method to a singlephase quasilinear Stefan problem with a forcing term. To construct the fully discrete approximation we apply the extrapolated Crank-Nicolson method and we derive the optimal order of convergence 2 in the temporal direction inL 2,H 1 normed spaces. 相似文献
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通过对方程组Ax=b的系数矩阵施行初等行变换,该文提出了解线性方程组Ax=b的一种新的预条件Gauss Seidel迭代方法,理论上证明了新的预条件Gauss Seidel迭代方法较经典的Gauss Seidel迭代法收敛速度快. 该文提出的新预条件方法推广了文[1-2]中提出的预条件方法,具体的数值例子说明了新预条件方法的有效性. 相似文献