APPROXIMATION PROPERTIES OF LAGRANGE INTERPOLATION POLYNOMIAL BASED ON THE ZEROS OF （1- x^2）cosnarccosx

We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.     

防洪坝根石缺石量计算模型

本文运用插值方法 ,给出了计算防洪坝根石缺石量的两种计算模型 .     

Shape-Preserving C 2 Functional Interpolation via Parametric Cubics

The paper proposes a method for the construction of a shape preserving C ² function interpolating a given set of data. The constructed interpolant is a parametric cubic curve. The shape of the curve can be easily controlled via tension parameters which have an immediate geometric interpretation. The approximation order is investigated and numerical examples are presented.     

Jacobi matrices with rapidly growing weights having only discrete spectrum

We establish sufficient conditions for self-adjointness on a class of unbounded Jacobi operators defined by matrices with main diagonal sequence of very slow growth and rapidly growing off-diagonal entries. With some additional assumptions, we also prove that these operators have only discrete spectrum.     

The heat equation to generate planar grids

An algorithm for the generation of quadrilateral grids on planar domains is presented. This algorithm is given by an iterative procedure, where, starting from an initial grid on the domain under consideration, the coordinates of the grid vertices are iteratively adjusted by using a local discrete variational approach. This procedure resembles the explicit difference scheme for a perturbed heat equation, where the perturbation can be dropped for convex domains. Experimental results on benchmark domains are presented, and show an interesting behavior of the proposed method.     

A new method for finding cycles by semilinear control

In the paper two new results that prove typically real and local univalent properties of certain class of rational functions in the unit disc $\mathbb{D}$ are presented. They provide a theoretical justification of a new method for finding periodic solutions of the discrete vector dynamical systems. The main goal of the paper is to propose and investigate the two-delays generalization of the scheme introduced by Ö. Morgül. The analysis shows that the coefficients in the proposed method can be chosen in a way that improves the admissible range of parameters. The method is elementary and easy to implement. Furthermore, numerical experiments with several well known maps show effectiveness of the control scheme.     

Postprocessing-based interpolation schemes for nested Cartesian finite difference grids of different size

Nested Cartesian grid systems by design require interpolation of solution fields from coarser to finer grid systems. While several choices are available, preserving accuracy, stability, and efficiency at the same time require careful design of the interpolation schemes. Given this context, a series of interpolation algorithms based on postprocessing halo information on nested Cartesian finite difference grids of different size were developed and tested. The results obtained indicate that most of these do not yield the expected improvement, and some even tend to make the solver unstable. However, some third- and fourth-order interpolation functions do yield considerable accuracy improvement, are stable, and are worth implementing.     

Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg–Landau equations

In this paper, we discuss the error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex space fractional Ginzburg-Landau equations. The continuous mass and energy inequalities as well as their discrete versions are presented. Moreover, by the discrete mass and energy inequalities, the error estimate of the Fourier pseudo-spectral scheme is established, and the scheme is proved to have the spectral accuracy.     

基于离散极大值法的太赫兹光谱特征吸收峰提取方法

太赫兹波在电磁波谱中介于微波和红外辐射之间，具有指纹特性、安全无损、强穿透性等特点，因此太赫兹光谱技术在药品成分和组成检测领域具有广泛应用价值。针对高纯度物质识别研究中存在部分弱吸收峰不易识别，以及混合物的太赫兹光谱中吸收峰强度降低而导致吸收峰位信息模糊化的问题，提出了一种基于离散极大值法的光谱吸收峰位识别方法，即伴随拐点法。伴随拐点法首先利用目标检测物太赫兹吸收系数谱图的一阶和二阶导数确定吸收峰位的伴随拐点和基线谱，其次将原始吸收光谱与基线谱进行差分运算得到差谱，最后根据离散极大值法确定吸收峰位，从而实现特征吸收峰的识别。为验证伴随拐点法的有效性，采用伴随拐点法对四种硝基呋喃类样品光谱进行吸收峰提取，并将吸收峰位识别结果与仿真结果进行比较。实验结果证明，伴随拐点法能有效识别目标检测物的强吸收峰和弱吸收峰。该方法不仅在含峰目标物的太赫兹特征吸收峰识别问题中具有广泛的应用前景，还适用于其他光谱的谱峰峰位检测。     

Reconstruction of Splines from Nonuniform Samples

In this paper, we study the reconstruction of spline functions from their nonuniform samples. We investigate the existence and uniqueness of the solution of the following problem: for given data {(x_n, y_n) : n ∈ Z}, find a cardinal spline f(x), of a given degree, satisfying yn = f(x_n), n ∈ Z.Several necessary and/or sufficient conditions for the existence and uniqueness of the solution of the problem are derived. Finally, an example and some applications are presented to illustrate the main results.