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本文我们研究线性周期抛物方程的有限元多格子动力学迭代.多格子动力学迭代又称多重网格波形松弛,它是在函数空间中的一种迭代过程.对于由加速技术得到的多格子动力学迭代算子,我们通过计算周期函数的Fourier系数给出了新的谱表达式.从这些有用的表达式出发,我们推导了时间连续和离散格式的迭代收敛条件.数值实验进一步验证了本文的理论结果. 相似文献
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关于线性互补问题的模系矩阵分裂迭代方法 总被引:1,自引:0,他引:1
模系矩阵分裂迭代方法是求解大型稀疏线性互补问题的有效方法之一.本文的目标是归纳总结模系矩阵分裂迭代方法的最新发展和已有成果,主要内容包括相应的多分裂迭代方法, 二级多分裂迭代方法和两步多分裂迭代方法, 以及这些方法的收敛理论. 相似文献
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首先证明了M-矩阵的H-相容分裂都是正则分裂,反之不成立.这表明对于M-矩阵而言,其正则分裂包含H-相容分裂.然后针对系数矩阵为M-矩阵的线性互补问题,建立了两个收敛定理:一是模系多分裂迭代方法关于正则分裂的收敛定理;二是模系二级多分裂迭代方法关于外迭代为正则分裂和内迭代为弱正则分裂的收敛定理. 相似文献
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在实一致光滑、一致凸Banach空间中提出了两种修正杂交迭代算法,证明了迭代序列既强收敛到极大单调算子的零点, 又强收敛到非扩展映射的不动点的结论. 推广和补充了以往的研究工作. 相似文献
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提出了偏微分方程有限差分逼近的数学Stencil 概念和Stencil消元策略, 建立了求解Poisson方程的新型迭代算法. 新算法与经典的Jacobi方法同样具有并行性质, 而且比Jacobi方法收敛快. 数值试验表明, 新算法达到同等误差精度所需时间比Jacobi方法和Gauss-Seidel方法都少; 而且新迭代法代替Jacobi方法应用于多重网格的磨光操作, 计算速度明显提高;另外多项式加速仍然适用于新迭代法. 相似文献
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对一致广义Lipschitz连续的逐次渐近Φ-强半压缩型有限算子簇,研究了一致光滑Banach空间中具误差的修正多步Noor迭代序列强收敛于该算子簇的公共不动点问题.作为所得结果的应用,得到了2007年Huang在相同空间框架中所建立的逼近具有有界值域的逐次Φ-强伪压缩算子的不动点具误差的修正Mann迭代和具误差的修正Ishikawa迭代两者的收敛是等价的这一结果,而且所用的方法不同于Huang.同时还改进和推广了Rhoades和Soltuz,Huang,Bu和Noor,Huang和Bu,Su,Yao,Chen和Zhou,Liu,Kim,Kim,Liu,Ni和Xu等人的近期相应结果. 相似文献
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Banach空间中极大单调算子零点的带误差项的新迭代格式 总被引:8,自引:0,他引:8
令E为实光滑、一致凸Banach空间,E为其对偶空间,AE×E为极大单调算子且A-10≠Φ.本文将引入新的迭代算法,并利用Lyapunov泛函,Qr算子与广义投影算子等技巧,证明了迭代序列弱收敛于极大单调算子A的零点的结论. 相似文献
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Lili Zhang 《计算数学(英文版)》2015,33(1):100-112
To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based synchronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an $H_+$-matrix, which improve the existing convergence theory. Numerical results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation. 相似文献
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Numerical Algorithms - In this paper, by using a modulus-based matrix splitting method as a smoother, a new modulus-based cascadic multigrid method is presented for solving elliptic variational... 相似文献
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Two-step modulus-based matrix splitting iteration method for linear complementarity problems 总被引:1,自引:0,他引:1
Li-Li Zhang 《Numerical Algorithms》2011,57(1):83-99
Bai has recently presented a modulus-based matrix splitting iteration method, which is a powerful alternative for solving
the large sparse linear complementarity problems. In this paper, we further present a two-step modulus-based matrix splitting
iteration method, which consists of a forward and a backward sweep. Its convergence theory is proved when the system matrix
is an H
+ -matrix. Moreover, for the two-step modulus-based relaxation iteration methods, more exact convergence domains are obtained
without restriction on the Jacobi matrix associated with the system matrix, which improve the existing convergence theory.
Numerical results show that the two-step modulus-based relaxation iteration methods are superior to the modulus-based relaxation
iteration methods for solving the large sparse linear complementarity problems. 相似文献
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P. Luo C. Rodrigo F. J. Gaspar C. W. Oosterlee 《Numerical Linear Algebra with Applications》2017,24(1)
A poroelastic saturated medium can be modeled by means of Biot's theory of consolidation. It describes the time‐dependent interaction between the deformation of porous material and the fluid flow inside of it. Here, for the efficient solution of the poroelastic equations, a multigrid method is employed with an Uzawa‐type iteration as the smoother. The Uzawa smoother is an equation‐wise procedure. It shall be interpreted as a combination of the symmetric Gauss‐Seidel smoothing for displacements, together with a Richardson iteration for the Schur complement in the pressure field. The Richardson iteration involves a relaxation parameter which affects the convergence speed, and has to be carefully determined. The analysis of the smoother is based on the framework of local Fourier analysis (LFA) and it allows us to provide an analytic bound of the smoothing factor of the Uzawa smoother as well as an optimal value of the relaxation parameter. Numerical experiments show that our upper bound provides a satisfactory estimate of the exact smoothing factor, and the selected relaxation parameter is optimal. In order to improve the convergence performance, the acceleration of multigrid by iterant recombination is taken into account. Numerical results confirm the efficiency and robustness of the acceleration scheme. 相似文献
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In order to solve large sparse linear complementarity problems on parallel multiprocessor systems, we construct modulus-based synchronous two-stage multisplitting iteration methods based on two-stage multisplittings of the system matrices. These iteration methods include the multisplitting relaxation methods such as Jacobi, Gauss–Seidel, SOR and AOR of the modulus type as special cases. We establish the convergence theory of these modulus-based synchronous two-stage multisplitting iteration methods and their relaxed variants when the system matrix is an H ?+?-matrix. Numerical results show that in terms of computing time the modulus-based synchronous two-stage multisplitting relaxation methods are more efficient than the modulus-based synchronous multisplitting relaxation methods in actual implementations. 相似文献
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In this paper, we study a nonlinear multigrid method for solving a general image denoising model with two L 1-regularization terms. Different from the previous studies, we give a simpler derivation of the dual formulation of the general model by augmented Lagrangian method. In order to improve the convergence rate of the proposed multigrid method, an improved dual iteration is proposed as its smoother. Furthermore, we apply the proposed method to the anisotropic ROF model and the anisotropic LLT model. We also give the local Fourier analysis (LFAs) of the Chambolle’s dual iterations and a modified smoother for solving these two models, respectively. Numerical results illustrate the efficiency of the proposed method and indicate that such a multigrid method is more suitable to deal with large-sized images. 相似文献
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Li-Li Zhang 《Journal of Optimization Theory and Applications》2014,160(1):189-203
The matrix multisplitting iteration method is an effective tool for solving large sparse linear complementarity problems. However, at each iteration step we have to solve a sequence of linear complementarity sub-problems exactly. In this paper, we present a two-stage multisplitting iteration method, in which the modulus-based matrix splitting iteration and its relaxed variants are employed as inner iterations to solve the linear complementarity sub-problems approximately. The convergence theorems of these two-stage multisplitting iteration methods are established. Numerical experiments show that the two-stage multisplitting relaxation methods are superior to the matrix multisplitting iteration methods in computing time, and can achieve a satisfactory parallel efficiency. 相似文献
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In this paper, a relaxation modulus-based matrix splitting iteration method is established, which covers the known general modulus-based matrix splitting iteration methods. The convergence analysis and the strategy of the choice of the parameters are given. Numerical examples show that the proposed methods are efficient and accelerate the convergence performance with less iteration steps and CPU times. 相似文献
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By employing modulus‐based matrix splitting iteration methods as smoothers, we establish modulus‐based multigrid methods for solving large sparse linear complementarity problems. The local Fourier analysis is used to quantitatively predict the asymptotic convergence factor of this class of multigrid methods. Numerical results indicate that the modulus‐based multigrid methods of the W‐cycle can achieve optimality in terms of both convergence factor and computing time, and their asymptotic convergence factors can be predicted perfectly by the local Fourier analysis of the corresponding modulus‐based two‐grid methods. 相似文献