A bivariate C2 Clough-Tocher scheme

A Clough-Tocher like interpolation scheme is described for values of position, gradient and hessian at scattered points in two variables. The domain is assumed to have been triangulated. The interpolant has local support, is globally twice differentiable, piecewise polynomial, and reproduces polynomials of degree up to three exactly.     

二元切触有理插值公式

降低切触有理插值的次数和解决切触有理插值函数的存在性是有理插值的一个重要问题。利用牛顿插值承袭性的思想和分段组合方法,构造出一种二元切触有理插值算法并推广到向量值有理插值,既解决了有理插值的存在性问题,又降低了切触有理插值函数的次数。相比于其他方法,算法的可行性是无条件的,有理插值函数次数较低,算法具有承袭性、计算量低、便于实际应用的特点。     

二元切触有理插值函数的构造方法

二元切触有理插值函数的构造方法大都是基于连分式进行的,其算法可行性是有条件的,且计算量较大,有理函数的次数较高。利用分段组合方法,构造出一种二元切触有理插值函数并将其推广到向量值切触有理插值情形,既解决了切触有理插值函数的存在性问题,又降低了切触有理插值函数的次数。相比于其他方法,其构造过程公式化,算法的可行性是无条件的,有理插值函数次数较低,且计算量较小,便于实际应用。     

A class of C 2piecewise quintic polynomials

A new class of C ² piecewise quintic interpolatory polynomials is defined. It is shown that this new class contains a number of interpolatory functions which present practical advantages, when compared with the conventional cubic spline.     

Shape control of a bivariate interpolating spline surface

A bivariate rational interpolation was constructed in earlier works using both function values and partial derivatives of the function being interpolated as the interpolation data, and it can be expressed by the symmetric basis. This paper gives the point-control method for modifying the interpolating surfaces by selecting suitable values of the parameters under the conditions that the interpolation data are not changed. An example is given to show the effectiveness of this method.     

New bivariate polynomial expansion with boundary data on the simplex

We introduce an extension to the two-dimensional simplex of the univariate two-point expansion formula for sufficiently smooth real functions introduced in [13]; it is a polynomial expansion with algebraic degree of exactness. This expansion is applied to obtain a new class of embedded boundary-type cubature formulae on the simplex.      

A simple nonparametric index of bivariate association for environmental data exploration

A purely data-based index for detecting bivariate association is proposed for preliminary data exploration when seeking to model a dependent variable, associated with a possibly large number of independent variables. No particular form of association between the dependent and independent variables is assumed. The proposed bivariate association index is the value p, which is the probability that a scatter plot created by an X-randomization will generate a smaller mean nearest neighbour distance. The rationale is that randomizing an existing X-Y association will result in a scatter plot which will usually have a greater mean nearest neighbour distance. The process is then repeated for all other independent variables to give a specific p for each one. A subset of potentially informative independent variables is then obtained by noting all those with low p values, but just how small p should be is left to the user.     

Construction of bivariate S-distributions with copulas

S-distributions are univariate statistical distributions with four parameters. They have a simple mathematical structure yet provide excellent approximations for many traditional distributions and also contain a multitude of distributional shapes without a traditional analog. S-distributions furthermore have a number of beneficial features, for instance, in terms of data classification and scaling properties. They provide an appealing compromise between generality in data representation and logistic simplicity and have been applied in a variety of fields from applied biostatistics to survival analysis and risk assessment. Given their advantages in the single- variable case, it is desirable to extend S-distributions to several variates. This article proposes such an extension. It focuses on bivariate distributions whose marginals are S-distributions, but it is clear how more than two variates are to be addressed. The construction of bivariate S- distributions utilizes copulas, which have been developed quite rapidly in recent years. It is demonstrated here how one may generate such copulas and employ them to construct and analyze bivariate—and, by extension, multivariate—S-distributions. Particular emphasis is placed on Archimedean copulas, because they are easy to implement, yet quite flexible in fitting a variety of distributional shapes. It is illustrated that the bivariate S-distributions thus constructed have considerable flexibility. They cover a variety of marginals and a wide range of dependences between the variates and facilitate the formulation of relationships between measures of dependence and model parameters. Several examples of marginals and copulas illustrate the flexibility of bivariate S-distributions.     

Kendall distributions and level sets in bivariate exchangeable survival models

For a given bivariate survival function , we study the relations between the set of the level curves of and the Kendall distribution. Then we characterize the survival models simultaneously admitting a specified Kendall distribution and a specified set of level curves. Attention will be restricted to exchangeable survival models.     

Efficient simulation of a bivariate exponential conditionals distribution

The bivariate distribution with exponential conditionals (BEC) is introduced by Arnold and Strauss [1988. Bivariate distributions with exponential conditionals, J. Amer. Statist. Assoc. 83, 522-527]. This work presents a simple and fast algorithm for simulating random variates from this density.     

A bivariate fuzzy time series model to forecast the TAIEX

Fuzzy time series models have been applied to forecast various domain problems and have been shown to forecast better than other models. Neural networks have been very popular in modeling nonlinear data. In addition, the bivariate models are believed to outperform the univariate models. Hence, this study intends to apply neural networks to fuzzy time series forecasting and to propose bivariate models in order to improve forecasting. The stock index and its corresponding index futures are taken as the inputs to forecast the stock index for the next day. Both in-sample estimation and out-of-sample forecasting are conducted. The proposed models are then compared with univariate models as well as other bivariate models. The empirical results show that one of the proposed models outperforms the many other models.     

A Bayesian semi-parametric bivariate failure time model

In this paper we introduce a Bayesian semiparametric model for bivariate and multivariate survival data. The marginal densities are well-known nonparametric survival models and the joint density is constructed via a mixture. Our construction also defines a copula and the properties of this new copula are studied. We also consider the model in the presence of covariates and, in particular, we find a simple generalisation of the widely used frailty model, which is based on a new bivariate gamma distribution.     

Cardinal interpolation: A bivariate polynomial example

The general interpolation problem over a linear space is solved by providing explicit formulas for the cardinal basis of the space. As an example of this technique, the cardinal form of a bivariate degree-nine polynomial interpolating to function and derivative values through order four at various points on a triangle is derived. The piecewise polynomial interpolant over an arbitrary triangulated domain in has C² continuity.     

局部形状可调插值曲线曲面及其参数选取方案

以形状可调插值曲线曲面为研究主题的文献多数侧重于分析曲线曲面性质,少有文献介绍可调插值曲线曲面的构造方法,以及调节参数的选取方案。这里以3次Hermite插值曲线为基础,通过在导矢中引入参数来构造形状可调插值曲线,将曲线按照插值数据进行整理,即可得到含参数的插值基函数,进而由之构造张量积插值曲面。为了帮助设计者寻找合适的参数,提供了4种用于确定曲线中形状参数的准则,其中的3种还推广应用于曲面,每种准则都提供了可以直接使用的公式。所给可调插值曲线曲面的构造方法以及参数选取方案具有一般性,数值实例验证了方案的有效性。     

基于变系数双变量模型的双变量阈值去噪法

针对不同子带小波系数的父子小波系数联合分布不同的特点,提出可描述这一特征的父子小波系数的变系数双变量分布模型,并使用贝叶斯最大后验估计理论推导出基于新模型的双变量阈值函数。结合具有平移不变性和多方向选择性的双树复小波变换以进一步提高图像的去噪效果。实验结果表明,与Sendur的双变量阈值法相比,新方法去噪后图像的PSNR值有了提高,图像的主观视觉效果也得到改善。     

Local hybrid approximation for scattered data fitting with bivariate splines

We suggest a local hybrid approximation scheme based on polynomials and radial basis functions, and use it to improve the scattered data fitting algorithm of (Davydov, O., Zeilfelder, F., 2004. Scattered data fitting by direct extension of local polynomials to bivariate splines. Adv. Comp. Math. 21, 223–271). Similar to that algorithm, the new method has linear computational complexity and is therefore suitable for large real world data. Numerical examples suggest that it can produce high quality artifact-free approximations that are more accurate than those given by the original method where pure polynomial local approximations are used.     

A trivariate clough—tocher scheme for tetrahedral data

An interpolation scheme is described for values of position, gradient and Hessian at scattered points in three variables. The domain is assumed to have been tesselated into tetrahedra. The interpolant has local support, is globally once differentiable, piecewise polynomial, and reproduces polynomials of degree up to three exactly. The scheme has been implemented in a FORTRAN research code.     

实现3D离散点优化三角划分的三维算法

本文系统研究了３Ｄ离散数据的直接三角划分，并解决了与多值曲面相对应离散数据的分片三角划分问题。实现这一算法的关键是将这些与多值曲面相对应的离散数据按有关的特征线分解，慢之转化成较简单的问题分别进行处理。目前，这种分片三角划分算法已在Ｂｅｚｉｅｒ三角曲面插值中取得了良好的效果。     

有理[2m+1,2m]型分段插值样条

常见的较低次有理带单形状因子分段有理插值样条通过代数运算,可用Bernstein基函数等价表示,这类分段插值样条利用Hermite插值的方法推广到高次有理[2m+1,2m]型,样条的生成曲线满足Cm-连续,并给出了具体的Bern-stein基函数表示方法的表达式,其形式较为简单,最后分别讨论了这类有理插值的逼近阶与约束域及保单调等方面的形状因子的选取情况,并给出了例子分析。