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1.
通过定义一种新的*-微分,本文给出了局部Lipschitz非光滑方程组的牛顿法,并对其全局收敛性进行了研究.该牛顿法结合了非光滑方程组的局部收敛性和全局收敛性.最后,我们把这种牛顿法应用到非光滑函数的光滑复合方程组问题上,得到了较好的收敛性. 相似文献
2.
本文研究了求解奇异非线性方程组的Levenberg-Marquardt方法的收敛性.利用选取新的迭代参数求解非线性方程组的L-M方法,获得点列的超线性收敛性和二阶收敛性,并把试验结果与文献[19,20]的结果进行了比较. 相似文献
3.
考虑了在一个柱形区域上的海洋动力学中二维黏性方程组解的收敛性.在此模型中存在一个关键的参数就是热源,众多周知,它的存在可能会使流体内层之间出现共振从而导致不稳定.因此,通过推导方程组的先验界,得到了方程组的解对热源自身的收敛性. 相似文献
4.
GSOR,GAOR,GSSOR和GSAOR 总被引:4,自引:0,他引:4
M.M.Martins于1986年提出了解线性代数方程组的MSOR方法,其实这种方法就是[2]中GAOR方法的特例,而且在[2]中还讨论了GSAOR方法,收敛性条件只含Jacobi迭代矩阵的谱半径,不含方程组的系数,特别是建立了GAOR或GSAOR收敛和方程组系数A为H阵的等价性,故所得结果比较好.又[1]中的定理1也是[4]中一个 相似文献
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6.
冯果忱 《高等学校计算数学学报》1980,(1)
热知,松弛法是解多变量方程组的有效方法之一,它广泛用于求解由偏微分方程离散化导出的方程组。1962年与1963年S.Schechter与作者曾各自独立地研究并发表了解非线性方程组的逐步松弛法(SOR方法)的收敛性,作者还研究了其它松弛程序的收敛性并且给出了敛速估计,1968年S.Schechter也进一步研究了其它松弛程序并估计了收敛速度。前述结果以及后来其它工作均假定方程组具有连续的Jacobi矩阵存在(参考[4])。本文在不假定Jacobi矩阵存在的条件下建立了松弛法大范围收敛性理沦,证明SOR—Newton法,SOR—弦截法及SOR—Steffensen法的收敛性,并给出了敛速估计,从而扩大了这类方法的适用范围,利用所得到的结果解决了描写受控核反应方程的差分及有限元模拟的松弛法的收敛性。 相似文献
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本文研究一类强耦合的奇异摄动对流扩散方程组的移动网格方法.首先,利用迎风有限差分格式对方程组进行离散.然后,推出数值解的后验误差估计,并以此设计出相应的自适应网格生成算法.同时,证明数值解具有一阶一致收敛性.最后,数值实验验证了本文移动网格方法的一致收敛性. 相似文献
9.
阻尼Gauss-Newton方法解非线性不等式组 总被引:1,自引:1,他引:0
本文研究了非线性不等式组的求解问题.利用了阻尼Gauss-Newton方法求解非线性方程组,获得了该算法的全局收敛性,推广了Gauss-Newton法在解非线性方程组方面的应用. 相似文献
10.
本文提出了一种求解等式约束非线性规划的新方法-线性代数方程组求解方法。我们证明了该算法具有全局收敛性和局部二阶收敛性。 相似文献
11.
通过递推关系,证明了解希尔伯特空间上的实系数非线性方程组的三阶方向牛顿法的半局部收敛性,给出了解的存在性以及先验误差界,最后计算出一些数值结果来证明我们的结论. 相似文献
12.
In this paper, we study a variant of the super-Halley method with fourth-order convergence for nonlinear equations in Banach
spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence
relations for the method are derived and then an existence-uniqueness theorem is given to establish the R-order of the method to be four and a priori error bounds. Finally, some numerical applications are presented to demonstrate
our approach. 相似文献
13.
In this paper, we study the semilocal convergence for a sixth-order variant of the Jarratt method for solving nonlinear equations
in Banach spaces. The semilocal convergence of this method is established by using recurrence relations. We derive the recurrence
relations for the method, and then prove an existence-uniqueness theorem, along with a priori error bounds which demonstrates
the R-order of the method. Finally, we give some numerical applications to demonstrate our approach. 相似文献
14.
The aim of this paper is to establish the semilocal convergence of a multipoint third order Newton-like method for solving F(x)=0 in Banach spaces by using recurrence relations. The convergence of this method is studied under the assumption that the second Fréchet derivative of F satisfies Hölder continuity condition. This continuity condition is milder than the usual Lipschitz continuity condition. A new family of recurrence relations are defined based on the two new constants which depend on the operator F. These recurrence relations give a priori error bounds for the method. Two numerical examples are worked out to demonstrate the applicability of the method in cases where the Lipschitz continuity condition over second derivative of F fails but Hölder continuity condition holds. 相似文献
15.
《Journal of Computational and Applied Mathematics》1998,98(2):305-309
We establish a convergence theorem for the Midpoint method using a new system of recurrence relations. The purpose of this note is to relax its convergence conditions. We also given an example where our convergence theorem can be applied but other ones cannot. 相似文献
16.
This paper focuses on the importance of center conditions on the first derivative of the operator involved in the solution of nonlinear equations by Newton’s method when the semilocal convergence of the method is established from the technique of recurrence relations. 相似文献
17.
A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works. 相似文献
18.
Paul Levrie 《Numerische Mathematik》1989,56(5):501-512
Summary In this paper we present a method of convergence acceleration for the calculation of non-dominant solutions of second-order linear recurrence relations for which the coefficients satisfy certain asymptotic conditions. It represents an improvement of the method recently proposed by Jacobsen and Waadeland [3, 4] for limit periodic continued fractions. For continued fractions the method corresponds to a repeated application of the Bauer-Muir transformation. Some examples and a generalization to non-homogeneous recurrence relations are given. 相似文献
19.
Xiuhua Wang Jisheng Kou Chuanqing Gu 《Journal of Optimization Theory and Applications》2012,153(3):779-793
In this paper, we consider the semilocal convergence of a class of modified super-Halley methods for solving nonlinear equations
in Banach spaces. The semilocal convergence of this class of methods is established by using recurrence relations. We construct
a system of recurrence relations for the methods, and based on it, we prove an existence–uniqueness theorem that shows the
R-order of the methods. 相似文献
20.
The semilocal convergence properties of Halley’s method for nonlinear operator equations are studied under the hypothesis that the second derivative satisfies some weak Lipschitz condition. The method employed in the present paper is based on a family of recurrence relations which will be satisfied by the involved operator. An application to a nonlinear Hammerstein integral equation of the second kind is provided. 相似文献