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基于构造非线性方程的牛顿迭代格式简便和牛顿迭代格式具有收敛快的特点,在解决实际问题时,牛顿迭代格式显得尤为重要,但是,牛顿迭代格式的初始值选取具有很大的局限性.利用泰勒级数展开,对牛顿迭代格式的收敛性进行分析,从而提出改进牛顿迭代格式的初始值选取方案,并利用不同的数值算例验证牛顿迭代格式收敛区域的改进方案的可行性,同时数值算例表明该方法具有操作简单的特点. 相似文献
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构造了一类新型的不带导数的牛顿迭代格式,通过建立误差方程,证明了该迭代格式至少是4阶收敛,同时获得了该迭代格式对应参数所满足的条件. 相似文献
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研究非线性算子方程的近似求解方法.首先对通常的求解非线性方程加速迭代格式进行推广,得到高阶收敛速度的加速迭代格式,最后把这种加速迭代格式推广到非线性算子方程的求解中去,利用非线性算子的渐进展开,证明了这种加速格式具有三阶的收敛速度. 相似文献
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§1.引言 一维搜索在非线性规划中非常重要,它常可归结为方程f′(x)=0的求解问题.本文基于牛顿反插值法对该问题提出了一个迭代求解格式,对于一般的n点迭代格式,该算法利用前n点的信息构造迭代的第n+1点.因此具有良好的局部收敛性;而且计算格式简单,易于计算机实现.数值试验表明,用三点格式已收敛得很快. 相似文献
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对于二维的Helmholtz方程,本文用联合紧致差分格式(CCD)离散,该差分格式具有六阶精度,三点差分和隐式的特点.本文基于CCD格式离散得到的线性系统和循环矩阵的快速傅里叶变换,提出了一种循环型预处理算子用于广义极小残量迭代算法(GMRES).给出了循环型预处理子的求解算法,证明了该预处理算子能使迭代算法具有较快的收敛速度.本文还与其他算法的预处理算子作比较,数值结果表明本文提出的循环型预处理算子具有更好的稳定性,并且对于较大的波数k,收敛速度也更快. 相似文献
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本文研究使用Ishikawa迭代格式求实李普希兹映射的不动点,指出该迭代格式仅具线性收敛率;对于参变量序列{αn}、{βn}所取的不同的值,比较了迭代格式的收敛速度.在给出加速因子定义的基础上,本文给出了加速收敛的一个充分条件. 相似文献
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《数学的实践与认识》2015,(11)
基于对牛顿迭代公式的改进及预估校正迭代的思想,提出了一种求解非线性方程的新的三阶预估-校正迭代格式.迭代公式无须计算函数的导数值,且理论上证明了它至少是三阶收敛的.数值实验验证了该迭代公式的有效性. 相似文献
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Using the forms of Newton iterative function, the iterative function of Newton's method to handle the problem of multiple roots and the Halley iterative function, we give a class of iterative formulae for solving equations in one variable in this paper and show that their convergence order is at least quadratic. At last we employ our methods to solve some non-linear equations and compare them with Newton's method and Halley's method. Numerical results show that our iteration schemes are convergent if we choose two suitable parametric functions λ(x) and μ(x). Therefore, our iteration schemes are feasible and effective. 相似文献
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本文对一维非线性 Schrödinger 方程给出两个紧致差分格式, 运用能量方法和两个新的分析技 巧证明格式关于离散质量和离散能量守恒, 而且在最大模意义下无条件收敛. 对非线性紧格式构造了 一个新的迭代算法, 证明了算法的收敛性, 并在此基础上给出一个新的线性化紧格式. 数值算例验证 了理论分析的正确性, 并通过外推进一步提高了数值解的精度. 相似文献
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Several splittings for non-Hermitian linear systems 总被引:3,自引:0,他引:3
Zhong-Zhi Bai 《中国科学A辑(英文版)》2008,51(8):1339-1348
For large sparse non-Hermitian positive definite system of linear equations,we present several variants of the Hermitian and skew-Hermitian splitting(HSS)about the coefficient matrix and establish correspondingly several HSS-based iterative schemes.Theoretical analyses show that these methods are convergent unconditionally to the exact solution of the referred system of linear equations,and they may show advantages on problems that the HSS method is ineffiective. 相似文献
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Mei-Chun Chen Po-Wen Hsieh Chun-Ting Li Yun-Tsz Wang 《Numerical Functional Analysis & Optimization》2013,34(5-6):436-461
This paper is mainly devoted to a comparative study of two iterative least-squares finite element schemes for solving the stationary incompressible Navier–Stokes equations with velocity boundary condition. Introducing vorticity as an additional unknown variable, we recast the Navier–Stokes problem into a first-order quasilinear velocity–vorticity–pressure system. Two Picard-type iterative least-squares finite element schemes are proposed to approximate the solution to the nonlinear first-order problem. In each iteration, we adopt the usual L 2 least-squares scheme or a weighted L 2 least-squares scheme to solve the corresponding Oseen problem and provide error estimates. We concentrate on two-dimensional model problems using continuous piecewise polynomial finite elements on uniform meshes for both iterative least-squares schemes. Numerical evidences show that the iterative L 2 least-squares scheme is somewhat suitable for low Reynolds number flow problems, whereas for flows with relatively higher Reynolds numbers the iterative weighted L 2 least-squares scheme seems to be better than the iterative L 2 least-squares scheme. Numerical simulations of the two-dimensional driven cavity flow are presented to demonstrate the effectiveness of the iterative least-squares finite element approach. 相似文献
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《Journal of the Egyptian Mathematical Society》2013,21(3):334-339
The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods. 相似文献
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We investigate full rank interpolatory vector subdivision schemes whose masks are positive definite on the unit circle except
the point z=1. Such masks are known to give rise to convergent schemes with a cardinal limit function in the scalar case.
In the full rank vector case, we show that there also exists a cardinal refinable function based on this mask, however, with
respect to a different notion of refinability which nevertheless also leads to an iterative scheme for the computation of
vector fields. Moreover, we show the existence of orthogonal scaling functions for multichannel wavelets and give a constructive
method to obtain these scaling functions.
AMS subject classification (2000) 42C40, 65T60, 65D05 相似文献
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This paper is concerned with the linear approximation method (i.e. the iterative method in which a sequence of vectors is generated by solving certain linearized subproblems) for solving the variational inequality. The global convergent iterative process is proposed by applying the continuation method, and the related problems are discussed. A convergent result is obtained for the approximation iteration (i.e. the iterative method in which a sequence of vectors is generated by solving certain linearized subproblems approximately). 相似文献
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Livinus U. Uko 《Mathematical Programming》1996,73(3):251-268
We give some convergence results on the generalized Newton method (referred to by some authors as Newton's method) and the
chord method when applied to generalized equations. The main results of the paper extend the classical Kantorovich results
on Newton's method to (nonsmooth) generalized equations. Our results also extend earlier results on nonsmooth equations due
to Eaves, Robinson, Josephy, Pang and Chan.
We also propose inner-iterative schemes for the computation of the generalized Newton iterates. These schemes generalize popular
iterative methods (Richardson's method, Jacobi's method and the Gauss-Seidel method) for the solution of linear equations
and linear complementarity problems and are shown to be convergent under natural generalizations of classical convergence
criteria.
Our results are applicable to equations involving single-valued functions and also to a class of generalized equations which
includes variational inequalities, nonlinear complementarity problems and some nonsmooth convex minimization problems. 相似文献