共查询到20条相似文献,搜索用时 109 毫秒
1.
提出一种求解无约束优化问题的非单调多步曲线搜索方法.此方法具有如下特点:(1)算法在产生下一个迭代点时不仅利用了当前迭代点的信息,而且还可能利用前m个迭代点的信息.这就是多步法;(2)下降方向和步长同时确定,而不是先找到方向,再由线性搜索寻找步长.这就是曲线搜索技术;(3)采用非单调搜索技巧.在较弱的条件下,我们证明了此方法的收敛性. 相似文献
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Lawrence E Levine Ray Maleh 《International Journal of Mathematical Education in Science & Technology》2013,44(5):781-786
It can be shown that if a differential equation is analytic near a point, then it is always possible to select a forcing term along with initial conditions that will ensure the solution to the new non-homogeneous equation is a polynomial that is the finite, truncated portion of the (infinite) series solution of the original equation. It turns out that this result can be extended to expansions about a singular point. The conditions under which such a polynomial truncation can be accomplished about a singular point are presented in the Appendix. A brief algorithm is described that enables one to choose the appropriate forcing term and initial conditions. Following this, an example involving Laguerre's equation is presented. 相似文献
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引用两种加速计算PageRank的算法,分别为内外迭代法和两步分裂迭代算法.从这两种方法中,得到多步幂法修正的内外迭代方法.首先,详细介绍了算法实施过程.然后,对此算法的收敛性进行证明,并且将此算法的谱半径与两步分裂迭代算法的谱半径进行比较.最后,数值试验说明该算法的计算速度比两步分裂迭代法要快. 相似文献
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We consider linear multi-step methods for stochastic ordinary differential equations and study their convergence properties for problems with small noise or additive noise. We present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations. In previous work, we considered Maruyama-type schemes, where only the increments of the driving Wiener process are used to discretize the diffusion part. Here, we suggest the improvement of the discretization of the diffusion part by also taking into account mixed classical-stochastic integrals. We show that the relation of the applied step sizes to the smallness of the noise is essential in deciding whether the new methods are worthwhile. Simulation results illustrate the theoretical findings. 相似文献
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在实自反Banach空间中,引入并研究一类k-次增生型变分包含问题,证明了这类变分包含解的存在与唯一性,并在去掉α_n→0,β_n→0(n→∝)以及序列{x_n)和{_η(g(x_n))}有界限制的条件下,建立了k-次增生型变分包含和变分不等式解的具有混合误差的多步迭代序列的强收敛性定理,给出了收敛率的估计式,从而改进和推广了前人的研究结果. 相似文献
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Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having
the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered
for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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I.A. Moghrabi 《Computational Optimization and Applications》2001,19(3):337-345
We consider multi-step quasi-Newton methods for unconstrained optimization. These methods were introduced by Ford and Moghrabi (Appl. Math., vol. 50, pp. 305–323, 1994; Optimization Methods and Software, vol. 2, pp. 357–370, 1993), who showed how interpolating curves could be used to derive a generalization of the Secant Equation (the relation normally employed in the construction of quasi-Newton methods). One of the most successful of these multi-step methods makes use of the current approximation to the Hessian to determine the parameterization of the interpolating curve in the variable-space and, hence, the generalized updating formula. In this paper, we investigate new parameterization techniques to the approximate Hessian, in an attempt to determine a better Hessian approximation at each iteration and, thus, improve the numerical performance of such algorithms. 相似文献
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Issam A. R. Moghrabi 《Journal of Mathematical Modelling and Algorithms》2007,6(2):231-238
The authors have derived what they termed quasi-Newton multi step methods in [2]. These methods have demonstrated substantial numerical improvements over the standard single step Secant-based BFGS. Such
methods use a variant of the Secant equation that the updated Hessian (or its inverse) satisfies at each iteration. In this
paper, new methods will be explored for which the updated Hessians satisfy multiple relations of the Secant-type. A rational
model is employed in developing the new methods. The model hosts a free parameter which is exploited in enforcing symmetry
on the updated Hessian approximation matrix thus obtained. The numerical performance of such techniques is then investigated
and compared to other methods. Our results are encouraging and the improvements incurred supercede those obtained from other
existing methods at minimal extra storage and computational overhead. 相似文献
11.
Mohammad Masjed-Jamei Zahra Moalemi Hari M. Srivastava Iván Area 《Mathematical Methods in the Applied Sciences》2020,43(3):1380-1398
In this paper, we first introduce a modification of linear multistep methods, which contain, in particular, the modified Adams-Bashforth methods for solving initial-value problems. The improved method is achieved by applying the Hermite quadrature rule instead of the Newton-Cotes quadrature formulas with equidistant nodes. The related coefficients of the method are then represented explicitly, the local error is given, and the order of the method is determined. If a numerical method is consistent and stable, then it is necessarily convergent. Moreover, a weighted type of the new method is introduced and proposed for solving a special case of the Cauchy problem for singular differential equations. Finally, several numerical examples and graphical representations are also given and compared. 相似文献
12.
We determine the existence and C
1 convergence of an inertial manifold for a strongly A(α) stable, pth order, p≧1, linear multi-step method approximating a sectorial evolution equation that satisfies a gap condition. This inertial manifold
gives rise to a one-step method that C
1 approximates the inertial form of the evolution equation and yields further approximation properties of the multi-step method.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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推广Lax-Wendroff多步方法,建立一类新的显式和隐式相结合的多步格式,并以此为基础提出了一类显隐多步-小波-Galerkin方法,可以用来求解依赖时间的偏微分方程.不同于Taylor-Galerkin方法,文中的方案在提高时间离散精度时不包含任何新的高阶导数.由于引入了隐式部分,与传统的多步方法相比该方案有更好的稳定性,适合于求解非线性偏微分方程,理论分析和数值例子都说明了方法的有效性. 相似文献
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Kai-tai Fang 《计算数学(英文版)》1999,(3)
1.IntroductionTheNumber-TheoreticMethod(NTM)isaspecialmethodwhichrepresentsacombinationofnumbertheoryandnumericalanalysis.Thewidestrangeofapplicationsandindeedthehistoricaloriginofthismethodisfoundinnumericalintegration.Alsorelatedproblemssuchajsinte... 相似文献
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1.引言实际问题中经常要遇到一族函数极小值问题的求解,即minfi(x),i=1,...,P;(1.1)其中人:R"、R具有公共的Hessian矩阵G(x)。7'fi(x),r是适中的数值.如在各种负载下的弹性体研究中,即要遇到问题(l.I)的求解,其中人(C)一人C)+qC十C;(=1,...,....对于不同的比则人(X)具有不同的极小点和不同的梯度D人(X),但具有相同的Hessian矩阵G(X).1994年,O'Leary等【']把拟一Newton算法推广至成组形式(multiPleversio...,… 相似文献
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解非线性方程组的一类离散的Newton算法 总被引:6,自引:0,他引:6
1.引言考虑非线性方程组设xi是当前的迭代点,为计算下一个迭代点,Newton法是求解方程若用差商代替导数,离散Newton法要解如下的方程其中这里为了计算J(;;h),需计算n‘个函数值.为了提高效能,Brown方法l‘]使用代入消元的办法来减少函数值计算量.它是再通过一次内选代从h得到下一个迭代点14+1.设n;=(《1,…,Zn尸,t二(ti,…,t*”,t为变量.BfOWll方法的基本思想如下.对人(x)在X;处做线性近似解出然后代入第二个函数,得到这是关于tZ,…,tn的函数.当(tZ,…,t。尸一(ZZ,…,Z。厂时,由(1.4),… 相似文献
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本文首先根据Runge-Kutta方法的思想,结合Newton迭代法,提出了一类带参数的解非线性方程组F(x)=0的迭代算法,然后基于解非线性方程f(x)=0的King算法,给出第二类解非线性方程组的迭代算法,收敛性分析表明这两类算法都是五阶收敛的.其次给出了本文两类算法的效率指数,以及一些已知算法的效率指数,并且将本文算法的效率指数与其它方法进行详细的比较,通过效率比率R_(i,j)可知本文算法具有较高的计算效率.最后给出了四个数值实例,将本文两类算法与现有的几种算法进行比较,实验结果说明本文算法收敛速度快,迭代次数少,有明显的优势. 相似文献
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Shi-ming Zheng 《计算数学(英文版)》2001,(4)
1. IntroductionLet F: RN --+ RN be a nonlinear map. Nixon)s methodand Chebyshev's methodare well known tor solved nothear equationwhere I is the "lift mains of order N, x is an approtoation of the solution x* of (1.3), x+ and& are new approAnations Of x* produced by Newton's and Chebyshev's methods, respectively.It is wen known that the order of convergence for Newton's ac chebyshev's methods is 2 and3, re8Pectively, if F'(x*) is nonSedar.Letbe a monic poly'nondal of degree N = Zn. The… 相似文献