非等距二元正交多项式回归

本文给出一种非街距二元正交多项式回归，从而将文「１」的结果推广到了二元情形。     

等重复数据的非等距正交多项式回归

本文给出了一种等重复数据情形下的非等距正交多项式回归模型。     

应用正交多项式设计法研究煤的粘附规律

丛茜等．应用正交多项式设计法研究煤的粘附规律．本文对影响煤与工作部件表面法向粘附力的二个主要因素：煤的含水量及所受正压力,进行了正交多项式回归设计,建立了显著的回归方程,并揭示了煤的粘附规律     

正交多项式及Pade逼近

利用Ｌｅｇｅｎｄｒｅ多项式的性质，得到ｅｘｐ（ｘ），ｔａｎｘ和ｔａｎｈｘ简单形式的对角Ｐａｄｅ逼近，在［－１，１］上Ｐｎ（ｘ）对于任意较低次幂的多项式是正交的·在求得某些函数的分母时，利用了Ｇａｕｓ求积公式·     

二元正交多项式小波的构造

本文中,给出了一个构造二元张量积正交多项式小波的构造准则,还给出了一个二元张量积正交多项式小波的例子.     

向量正交多项式的行列式表示

本文指出了代数Ｈｅｒｍｉｔｅ－Ｐａｄｅ逼近与向量正交多项式的关系，构造了计算向量正交多项式的行列式表示，并通过具体算例验证了它的正确性．     

用Zernike多项式进行波面拟合的一种新算法

该文提出了一种用于计算全息数字波面干涉仪中实现波面Ｚｅｒｎｉｋｅ多项式拟合的精确算法。该算法不同于传统的直接构造方程和Ｇｒａｍ－Ｓｃｈｍｉｄｔ正交化方法,而是用Ｈｏｕｓｅｈｏｌｄｅｒ变换对矛盾方程的广义增广矩阵进行正交三角化,直接求解拟合系数。它避免了构造法方程组,从而避免了以前的方法因构造的法方程组出现严重病态而引入的计算误差,并且易于编程,因而是一种比较理想的实现Ｚｅｒｎｉｋｅ多项式拟合的算法     

Gram-Schmidt 正交基的行列式表示法

Gram-Schmidt正交化方法是求正交基的一种算法.基于行列式的性质和归纳法可以证明,其正交向量组的一般项可通过行列式表示出来.     

有限域上一类多项式组的正交性

研究了有限域上一类特殊的多项式组,通过特征和给出了若干判定其正交性的充分条件,从而可以用来构建这种类型的正交多项式组.     

应用正交多项式设计法研究煤的粘附

本文对影响煤与工作部件表面法向粘附力的二个主要因素：煤的含水量及所受正压力,进行了正交多项式回归设计,建立了显著的回归方程,并揭示了煤的粘附规律。     

Recursive Estimation of Regression Functions by Local Polynomial Fitting

The recursive estimation of the regression function m(x) = E(Y/X = x) and its derivatives is studied under dependence conditions. The examined method of nonparametric estimation is a recursive version of the estimator based on locally weighted polynomial fitting, that in recent articles has proved to be an attractive technique and has advantages over other popular estimation techniques. For strongly mixing processes, expressions for the bias and variance of these estimators are given and asymptotic normality is established. Finally, a simulation study illustrates the proposed estimation method.     

Lebesgue Constraints for an Orthogonal Polynomial Schauder Basis

We examine a certain class of Schauder bases for the space C[-1,1] consisting of algebraic polynomials orthogonal with respect to theChebycheff weight of the first kind. We give an improved estimate for itsLebesgue constants.     

Representation of Polynomials by Linear Combinations of Radial Basis Functions

Let ${\mathcal {P}_{n}^{d}}$ denote the space of polynomials on ? ^d of total degree n. In this work, we introduce the space of polynomials ${\mathcal {Q}_{2 n}^{d}}$ such that ${\mathcal {P}_{n}^{d}}\subset {\mathcal {Q}_{2 n}^{d}}\subset\mathcal{P}_{2n}^{d}$ and which satisfy the following statement: Let h be any fixed univariate even polynomial of degree n and $\mathcal{A}$ be a finite set in ? ^d . Then every polynomial P from the space  ${\mathcal {Q}_{2 n}^{d}}$ may be represented by a linear combination of radial basis functions of the form h(∥x+a∥), $a\in \mathcal{A}$ , if and only if the set $\mathcal{A}$ is a uniqueness set for the space  ${\mathcal {Q}_{2 n}^{d}}$ .     

A Quasi-Interpolation Satisfying Quadratic Polynomial Reproduction with Radial Basis Functions

In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.     

Simultaneous Preservation of Orthogonality of Polynomials by Linear Operators Arising from Dilation of Orthogonal Polynomial Systems

For an orthogonal polynomial system and a sequence of nonzero numbers,let be the linear operator defined on the linear spaceof all polynomials via for all .We investigate conditions on and under which can simultaneously preserve the orthogonality ofdifferent polynomial systems. As an application, we get that for , a generalized Laguerre polynomial system, no can simultaneously preserve the orthogonality of twoadditional Laguerre systems, and , where and . On the other hand, for ,the Chebyshev polynomial system and , simultaneously preserves the orthogonality of uncountablymany kernel polynomial systems associated with p. We study manyother examples of this type.     

不同阶次连带勒让德函数的正交性

根据连带勒让德函数的递推公式和基本性质,本文详细推导了不同阶次连带勒让德函数pkn(x)与plm(x)在闭区间[-1,1]上关于权函数ω(x)=(1-x2)k2-l的正交性.当k=l时,结论退化为pkn(x)在[-1,1]上关于权ω(x)=1的正交性.     

Optimization of Polynomial Fractional Functions

A new approach is proposed for optimizing a polynomial fractional function under polynomial constraints, or more generally, a synomial fractional function under synomial constraints. The approach is based on reformulating the problem as the optimization of an increasing function under monotonic constraints.