抛物型方程的自适应正交配置算法

本文针对抛物型方程数值解不稳定的问题,利用牛顿迭代法来求解隐式Euler方法所给出的离散格式,获得了数值解较为稳定的抛物型方程自适应正交配置算法.     

有关超越亚纯函数迭代理论的研究

英国数学家Ｉ.Ｂａｋｅｒ研究了超越整函数的迭代的极限函数有关复动力系统性质．本文将把Ｉ．Ｂａｋｅｒ的工作推广到亚纯函数,主要结果有：ｆ（ｘ）是亚纯函数,如果函数数列ｆｎ（ｚ）的任意收敛的子数列在Ｆ（ｆ）的分支上的极限函数是常数,则该常数一定属于集合Ｅ（ｆ）ＵＥ’（ｆ）Ｕ等,     

长旋转椭球波函数本征值的精确计算

利用数值迭代技术给出了长旋转椭球波函数本征值的精确求解方法.当 c≤5时,本文的计算结果与文献[4]给出的数值吻合得很好,且具有更高的精度.给出的方法可以精确地求解 c<10时长旋转椭球波函数的本征值,计算精度达到10~(-14)。     

Strong orthogonal decompositions and non‐linear impulse response functions for infinite‐variance processes

The author proves that Wold‐type decompositions with strong orthogonal prediction innovations exist in smooth, reflexive Banach spaces of discrete time processes if and only if the projection operator generating the innovations satisfies the property of iterations. His theory includes as special cases all previous Wold‐type decompositions of discrete time processes, completely characterizes when non‐linear heavy‐tailed processes obtain a strong‐orthogonal moving average representation, and easily promotes a theory of non‐linear impulse response functions for infinite‐variance processes. The author exemplifies his theory by developing a non‐linear impulse response function for smooth transition threshold processes, and discusses how to test decomposition innovations for strong orthogonality and whether the proposed model represents the best predictor. A data set on currency exchange rates allows him to illustrate his methodology.     

二元递归关系的迭代与多重和

本文应用迭代法求解组合分析中一些二元递归关系,导出了得到它们的解的多重和算式。     

Banach空间中非线性不适定问题的Levenberg-Marquardt迭代法

基于已有的Banach空间非线性不适定问题的迭代法,给出了Levenberg-Marquardt迭代法的表达式,研究了它的收敛性.利用先验条件、源条件和广义的Bregman距离,分别证明了Levenberg-Marquardt迭代法的强收敛性和关于Bregman距离的收敛性.     

双曲型偏微分方程的变分迭代解法

讨论双曲型偏微分方程的定解问题,应用改进的变分迭代算法可以得到这类方程的精确解或近似解析解,同传统的数值方法相比,这种算法计算量小而且收敛速度快.     

Inference for Log-Gamma Distribution Based on Progressively Type-II Censored Data

We discuss the maximum likelihood estimates (MLEs) of the parameters of the log-gamma distribution based on progressively Type-II censored samples. We use the profile likelihood approach to tackle the problem of the estimation of the shape parameter κ. We derive approximate maximum likelihood estimators of the parameters μ and σ and use them as initial values in the determination of the MLEs through the Newton–Raphson method. Next, we discuss the EM algorithm and propose a modified EM algorithm for the determination of the MLEs. A simulation study is conducted to evaluate the bias and mean square error of these estimators and examine their behavior as the progressive censoring scheme and the shape parameter vary. We also discuss the interval estimation of the parameters μ and σ and show that the intervals based on the asymptotic normality of MLEs have very poor probability coverages for small values of m. Finally, we present two examples to illustrate all the methods of inference discussed in this paper.     

Fixed Point Iteration for Estimating the Parameters of Extreme Value Distributions

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this article using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton–Raphson approach which requires differentiation unlike the fixed point iteration which is also easier to implement. Graphical approaches are also usually proposed in the literature. We prove that these reduce in fact to the fixed point solution proposed in this article.     

变分迭代算法的应用

介绍了一种对求解非线性方程非常有效的方法-变分迭代算法及其发展成果．几个例子说明这种方法的有效性．