NEWTON—AOR方法的收敛性

本文将解线性方程组的AOR迭代法推广到解非线性方程组,构造和研究了Newton-AOR方法,建立了收敛性定理和比较定理,在一定条件下,从理论上证明了Newton—AOR方法比Newton—SOR方法收敛快,并给出了数值例子。文中所用有关概念和记号的意义见[1]。     

一类预条件AOR迭代法的收敛性分析

本文研究了线性方程组Ax=b的预条件迭代法.利用新的待定参数加速预条件子的方法,获得了一种带参数的新预条件迭代法,并对参数的选择给出必要条件,证明了对于非奇异不可约M-矩阵,新预条件方法收敛且可以加速AOR迭代法的收敛速度,数值例子表明新预条件方法是有效的,推广了已有文献中的有关结果.     

AOR方法的收敛性定理

获得了著名的AOR方法收敛的实用条件和H矩阵的实用判别条件。所得AOR方法的收敛条件便于实际计算应用,适用范围不要求方程组系数矩阵对角占优,适用于数学物理问题中广泛的矩阵类。给出的数值例子表明了所得结果的实用性。     

块AOR迭代法的收敛性

本文推广了解线性方程组的AOR迭代法,给出了块AOR迭代法(BAOR迭代法).文中引进了块M-矩阵,块H-矩阵,块严格对角优势矩阵,块Hermite正定矩阵,块相容次序矩阵和广义块相容次序矩阵等概念.在线性方程组的系数矩阵分别具有上述性质的假设下,讨论了BAOR迭代法的敛散性.     

一类预条件AOR迭代法及其收敛性

给出了一类预条件的AOR迭代法及其收敛性,并给出了松驰因子ω与加速因子γ的选取对收敛速度的影响,同时通过数值实例验证了主要结果.     

循环矩阵和AOR方法的敛散区域

§1.引言解线性方程组通常采用迭代法 1978年,HadjidimosA.在[1]中提出了Accelerated Overrelaxation Method(简其中D、L、U分别为A的对角部分、严格下和严格上三角部分,则AOR方法的迭代矩阵为     

解非线性方程组的并行多重分裂区间AOR方法

解线性方程组与非线性方程组的并行分裂算法是适合于并行计算的一类很有效算法,Frommer和Mayer将它用于求解线性区间方程组。本文将并行多重分裂方法与求解非线性方程组的区间松弛法结合,得到了一类适合并行计算的区间松弛法,称为并行多重分裂区间AOR方法(简称PMI—AOR方法)。文中构造的并行多重分裂Krawczyk型区间     

关于AOR迭代法的研究

本文论证了严格对角占优矩阵之AOR法的误差估计式中的误差估计常数hγ,ω（0≤γ≤ω0）的最小值是h1,1.     

L-矩阵的多参数预条件AOR迭代法

最近王广彬等人讨论了在预条件因子P=I+S′作用下的预条件AOR方法,推广了他们的预条件因子,提出了一个多参数的预条件因子P_α=I+S_α,并建立了新的预条件AOR迭代法与经典的AOR迭代法的比较定理.     

Convergence Domains of AOR Type Iterative Matrices for Solving Non-Hermitian Linear Systems

We discuss AOR type iterative methods for solving non-Hermitian linear systems based on Hermitian splitting and skew-Hermitian splitting. Convergence domains of iterative matrices are given and optimal parameters are investigated for skew-Hermitian splitting. Numerical examples are presented to compare the effectiveness of the iterative methods in different points in the domain. In addition, a model problem of three-dimensional convection-diffusion equation is used to illustrated the application of our results.     

On bounds for the mode and median of the generalized hyperbolic and related distributions

Except for certain parameter values, a closed form formula for the mode of the generalized hyperbolic (GH) distribution is not available. In this paper, we exploit results from the literature on modified Bessel functions and their ratios to obtain simple but tight two-sided inequalities for the mode of the GH distribution for general parameter values. As a special case, we deduce tight two-sided inequalities for the mode of the variance-gamma (VG) distribution, and through a similar approach we also obtain tight two-sided inequalities for the mode of the McKay Type I distribution. The analogous problem for the median is more challenging, but we conjecture some monotonicity results for the median of the VG and McKay Type I distributions, from we which we conjecture some tight two-sided inequalities for their medians. Numerical experiments support these conjectures and also lead us to a conjectured tight lower bound for the median of the GH distribution.     

Fractional variational problems with the Riesz-Caputo derivative

In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the functional is different from the interval of the fractional derivative. Next we consider integral dynamic constraints on the problem, for several different cases. Finally, we determine optimality conditions for functionals depending not only on the admissible functions, but on time also, and we present a necessary condition for a pair function-time to be an optimal solution to the problem.     

Function spaces in metrically generated theories

The theory of metrically generated constructs provides us with an excellent setting for the study of function spaces. In this paper we develop a function space theory for metrically generated constructs and, by considering different metrically generated constructs, we capture interesting examples. For instance, for uniform spaces we retrieve the uniformity of uniform convergence and its generalization to Σ-convergence and for UG-spaces we obtain a quantified version of these structures. Our theory also allows for many applications, in particular we are able to characterize the complete subspaces of these function spaces and we succeed in producing an appropriate Ascoli theorem.     

可逆矩阵的高次伴随矩阵

用数学归纳法推出了可逆矩阵的高次伴随矩阵的公式,并结合可逆矩阵的基本公式得出了可逆矩阵的高次伴随矩阵的行列式和逆矩阵,给出了可逆矩阵的高次伴随矩阵的特征值和特征向量的表示公式,最后讨论了若干个可逆矩阵的乘积的高次伴随矩阵.     

Minimal polynomial systems for parametric matrices

In this article, we study the minimal polynomials of parametric matrices. Using the concept of (comprehensive) Gröbner systems for parametric ideals, we introduce the notion of a minimal polynomial system for a parametric matrix, i.e. we decompose the space of parameters into a finite set of cells and for each cell we give the corresponding minimal polynomial of the matrix. We also present an algorithm for computing a minimal polynomial system for a given parametric matrix.     

Functional limit theorems for generalized quadratic variations of Gaussian processes

In this paper, we establish functional convergence theorems for second order quadratic variations of Gaussian processes which admit a singularity function. First, we prove a functional almost sure convergence theorem, and a functional central limit theorem, for the process of second order quadratic variations, and we illustrate these results with the example of the fractional Brownian sheet (FBS). Second, we do the same study for the process of localized second order quadratic variations, and we apply the results to the multifractional Brownian motion (MBM).     

Towards a self-consistent theory of volatility

In this paper, we propose a new theory for the formation of volatility which takes into account the influence of option hedging on the assets price dynamics. By analogy with statistical mechanics, we build a self-consistent equation for the volatility, we show it is well-posed and we explain how it can be solved.     

对角形拟线性椭圆方程组的一般特征问题

本文对拟线性椭圆方程组的一般特征问题得到极小解在L∞中的界,并利用变分方法证明了它的极小解的存在性.     

A Class of differential inverse variational inequalities in finite dimensional spaces

In this paper, we study a class of differential inverse variational inequality (for short, DIVI) in finite dimensional Euclidean spaces. Firstly, under some suitable assumptions, we obtain linear growth of the solution set for the inverse variational inequalities. Secondly, we prove existence theorems for weak solutions of the DIVI in the weak sense of Carath\"{e}odory by using measurable selection lemma. Thirdly, by employing the results from differential inclusions we establish a convergence result on Euler time dependent procedure for solving the DIVI. Finally, we give a numerical experiment to verify the validity of the algorithm.     

Optimal harvesting for nonlinear age-dependent population dynamics

In this paper, we investigate an optimal harvesting problem for nonlinear age-dependent population dynamics. Using the concept of the normal cone, we also obtain the necessary conditions for optimality for the optimal control problem. Using Ekeland’s variational principle, we demonstrate the existence and uniqueness of solutions for the optimal control problem. Finally, we give the synthesis of the optimal feedback law.