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本文研究分别由x_(n+1)=f(x_n),x_(n+1)=f(x_n,x_(n-1)),及g(x_(n+1))=f(x_n)产生的迭代数列收敛性问题,并运用构造迭代数列的方法解决一些实际问题. 相似文献
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利用函数单调递增对递推数列xn+1=f(xn)单调性进行讨论,在对递推数列收敛性作分析的基础上,得到使得递推数列收敛的初始迭代值的区域,讨论的方法可以用于类似问题的研究. 相似文献
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递推数列x_(n+1)=f(x_n)的单调性与收敛性讨论 总被引:1,自引:0,他引:1
利用函数单调递增对递推数列xn+1=f(xn)单调性进行讨论,在对递推数列收敛性作分析的基础上,得到使得递推数列收敛的初始迭代值的区域,讨论的方法可以用于类似问题的研究. 相似文献
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从迭代数列及其基本性质出发,给出单调有界定理、压缩映象原理、Cauchy收敛准则和上(下)极限四种判别迭代数列收敛的方法. 相似文献
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数学竞赛中的递推数列问题 总被引:1,自引:0,他引:1
在各级各类的数学竞赛中 ,大量的数列问题都是由递推关系给出的 .建立递推关系是研究数列的各种性质以及许多综合数学问题的有效手段 (例如某些组合数的计算问题 ) .因此 ,运用递推关系解决问题是一种非常重要的途径 .本文我们讨论处理递推关系的一些常用方法 .1 迭代法 迭代法就是反复运用题设所给数列 {an}的递推关系进行代换 ,每代一次 ,脚标n就往下降 ,直到能用初始值表示an 为止 .但是在大多数情况下 ,迭代之后不能写成简单的形式 ,因此迭代不出任何结果 ,这时也可考虑进行适当的变换 ,然后再进行迭代 .例 1 (1996年全国高中… 相似文献
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函数迭代问题是各级各类考试和竞赛中的常见题型,是中学数学教与学的难点.这类问题常用不完全归纳法求解,但往往不能揭示其一般规律.其实,如能将其转化为给出递推关系的数列问题,再利用数列的有关知识可使这类问题简捷、巧妙地获解.现举例解析如下: 相似文献
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A class of modified regula falsi iterative formulae for solving nonlinear equations is presented in this paper. This method is shown to be quadratically convergent for the sequence of diameters and the sequence of iterative points. The numerical experiments show that new method is effective and comparable to well-known methods. 相似文献
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令E为实光滑、一致凸Banach空间,E为其对偶空间.令Ai E×E,i=1,2,…,m,为极大单调算子且∩mi=1Ai-10≠.将引进一个新定义、给出一种新迭代算法,并利用Lyapunov泛函与广义投影算子等技巧,证明迭代序列强收敛于Ai的公共零点,i=1,2,…,m.去掉了以往结论中过强的限定条件,是对笔者以往工作的延续。 相似文献
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Yuan‐Ming Wang Cui‐Xia Liang Ravi P. Agarwal 《Numerical Methods for Partial Differential Equations》2011,27(3):680-701
The aim of this article is to develop a new block monotone iterative method for the numerical solutions of a nonlinear elliptic boundary value problem. The boundary value problem is discretized into a system of nonlinear algebraic equations, and a block monotone iterative method is established for the system using an upper solution or a lower solution as the initial iteration. The sequence of iterations can be computed in a parallel fashion and converge monotonically to a maximal solution or a minimal solution of the system. Three theoretical comparison results are given for the sequences from the proposed method and the block Jacobi monotone iterative method. The comparison results show that the sequence from the proposed method converges faster than the corresponding sequence given by the block Jacobi monotone iterative method. A simple and easily verified condition is obtained to guarantee a geometric convergence of the block monotone iterations. The numerical results demonstrate advantages of this new approach. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
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This paper deals with a new algorithm for a 0-1 bidimensional knapsack Lagrangean dual which relaxes one of the two constraints.
Classical iterative algorithms generate a sequence of multipliers which converges to an optimal one. In this way, these methods
generate a sequence of 0-1 one-dimensional knapsack instances. Generally, the procedure for solving each instance is considered
as a black box. We propose to design a new iterative scheme in which the computation of the step size takes into account the
algorithmic efficiency of each instance. Our adapted step size iterative algorithm is compared favorably with several other
algorithms for the 0-1 biknapsack Lagrangean dual over difficult instances for CPLEX 7.0. 相似文献
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关于序列的不等式及其应用 总被引:4,自引:0,他引:4
本文证明了一些关于新的序列的不等式.作为定理的应用,引进了一类新的迭 代序列并证明了它的收敛性.进一步地,证明了它与著名的Ishikawa迭代序列等价. 相似文献
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本文引入一类关于模糊(Fuzzy)映象的新的广义补余问题,构造出一类新的迭代算法.我们讨论这类广义补余问题解的存在性及迭代序列的收敛性. 相似文献
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In this paper, we introduce and study a new class of generalized mixed variational-like inequality for random fuzzy mappings(GMVLIP). An existence theorem for auxiliary problem of the GMVLIP is established. Further, by exploiting the theorem, we construct and analyze a new iterative algorithm for finding the solution of the GMVLIP. Furthermore, we prove the existence of a unique solution of the GMVLIP and discuss the convergence analysis of iterative sequence generated by the iterative algorithm. 相似文献
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曾六川 《高校应用数学学报(英文版)》2003,18(3):283-286
Let(X,‖·‖ ) be a Banach space.Let K be a nonempty closed,convex subset of Xand T∶K→K.Assume that T is Lipschitzian,i.e.there exists L>0 such that‖ T(x) -T(y)‖≤ L‖ x -y‖for all x,y∈K.Withoutloss of generality,assume that L≥ 1 .Assume also that T is strictly pseudocontractive.According to[1 ] this may be statedas:there exists k∈ (0 ,1 ) such that‖ x -y‖≤‖ x -y + r[(I -T -k I) x -(I -T -k I) y]‖for all r>0 and all x,y∈ K.Throughout,let N denote the set of positive in… 相似文献