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关于不用计算导数的大范围收敛迭代法的注记   总被引:13,自引:2,他引:11  
1 引  言在文 [1 ]中我们借助于动力系统方法导出了求连续函数 f(x)在区间 [a ,b]上单零点x 的一个大范围收敛的连续性方法 .此处 f(x)满足李氏条件 ,且 f(a) <0 ,f(b) >0 .这个连续性方法由动力系统dxdt =- f(x)x( 0 ) =x0 ∈ [a ,b]( 1 )确定 ,其解析解x(t ,x0 )具有性质limt→ +∞x(t,x0 ) =x ,  x0 ∈ [a ,b].  为了数值地求出x ,我们利用显式欧拉法xn+ 1=xn -hnf(xn)x0 =b ora ( 2 )来求 ( 1 )式的解 .其中hn>0 ,为步长 .它的选择满足文 [1 ]中的不等式a<xn+ 1<xn,…  相似文献
2.
关于MQ算法的松驰因子   总被引:1,自引:0,他引:1  
王寿城 《东北数学》2005,21(4):404-410
In this paper, a new method, so called A-method, is given for the convergence analysis of the MQ-algorithm. And the finer relaxation parameter θA is obtained. The numerical results show that our new method has the outstanding effect of accelerating convergence. Moreover, the relaxation parameter θA is the optimum in a point of view.  相似文献
3.
本文证明了[2]提出的两种连分式加速收敛方法等价性的一般猜想是正确的。  相似文献
4.
Landweber iterative methods for angle-limited image reconstruction   总被引:1,自引:0,他引:1  
We introduce a general iterative scheme for angle-limited image reconstruction based on Landwebet's method. We derive a representation formula for this scheme and consequently establish its convergence conditions. Our results suggest certain relaxation strategies for an accelerated convergence for angle-limited image reconstruction in L^2-norm comparing with alternative projection methods. The convolution-backprojection algorithm is given for this iterative process.  相似文献
5.
The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization problem. To improve the efficiency, we set about from quadratic interpolation, combine the advantage of the quadratic convergence rate of Newton's method and adopt the idea of Anderson-Bjorck extrapolation, then we present a rapidly convergence algorithm and give its corresponding convergence conclusions. Finally we did the numerical experiments with the some well-known test functions for optimization and the application test of the ANN learning examples. The experiment results showed the validity of the algorithm.  相似文献
6.
本文获得了一类极限循环连分式的加速收敛因子,证明了它们具有良好的加速收敛性质.  相似文献
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