Newton-Like Iteration Based on a Cubic Polynomial for Structured Matrices

We recall Newtons iteration for computing the inverse or Moore–Penrose generalized inverse of a matrix. Then we specialize this approach to the case of structured matrices where all input, output and intermediate auxiliary matrices are represented in a compressed form, via their short displacement generators. We design a new Newton-like iteration based on a cubic polynomial and show its effectiveness by some numerical experiments for matrices from the Toeplitz-like class and the Cauchy-like class.     

Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

In this article, we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces. The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.     

PICARD ITERATION FOR NONSMOOTH EQUATIONS

1. IntroductionConsider the following nonsmooth equationsF(x) = 0 (l)where F: R" - R" is LipsChitz continuous. A lot of work has been done and is bellg doneto deal with (1). It is basicly a genera1ization of the cIassic Newton method [8,10,11,14],Newton-lthe methods[1,18] and quasiNewton methods [6,7]. As it is discussed in [7], the latter,quasiNewton methods, seem to be lindted when aPplied to nonsmooth caJse in that a boundof the deterioration of uPdating matrir can not be maintained w…     

The variational iteration method for solitary patterns solutions of gBBM equation

We consider solitary patterns solutions of generalized Benjamin–Bona–Mahony equations (shortly gBBM). The variational iteration method (shortly VIM) is applied for the numerical solution subject to appropriate initial condition. The numerical solutions of our model equation are calculated in the form of convergence power series with easily computable components. The VIM performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability.     

直接解调成像的快速算法

直接解调方法(Direct Demodulate Method, DD)中运用的最多的迭代方法是Richardson-Lucy (RL)迭代. RL迭代的公式可以改写成矩阵形式, 其中包含了主要计算量的两次矩阵乘法在点扩展函数满足平移不变性的情况下可以写成卷积的形式, 而卷积可以使用快速傅里叶变换(Fast Fourier Transform, FFT)做快速计算. 详细介绍了上述过程, 并将该方法应用到了硬X射线调制望远镜(Hard X-ray Modulate Telescope,HXMT)的DD成像中, 通过理论的和模拟的计算对比了优化前后DD方法对计算资源的开销.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

Stability of symmetric closed characteristics on symmetric compact convex hypersurfaces in ℝ<Superscript>2<Emphasis Type="Italic">n</Emphasis></Superscript> under a pinching condition

In this paper, let Σ R2n be a symmetric compact convex hypersurface which is ( r, R )- pinched with R/r (5/3)1/2 . Then Σ carries at least two elliptic symmetric closed characteristics; moreover, Σ carries at least E [ n-1/2 ] + E [ n-1/3 ] non-hyperbolic symmetric closed characteristics.     

非线性Duffing方程的高精度近似解

由参数迭代法得到非线性Duffing方程的高精度近似解,即使在小参数ε＝1的强非线性情况下,方程的误差函数在整个解域小于1％     

用逐次逼近迭代法分析含空间滤波器的多程激光放大系统的逆问题

基于Ｆｒａｎｔｚ－Ｎｏｄｖｉｋ（Ｆ－Ｎ）方程和广义惠更斯－菲涅耳衍射积分，提出了解决含空间滤波器的多程激光放大系统的逆问题的迭代算法，并作了数值计算了，所得的数值计算方法和有关结果可用于高功率多程激光放大系统的设计。     

一般非线性渗流方程正性的扩展

本文研究一般非线性渗流方程解的一种性态.利用De Giorgi方法与BCP估计相结合,得到了一般非线性渗流方程正性的扩展性质,推广了非线性渗流方程的结果.