1.

ON AN EXTENSION OF ABELGONTSCHAROFF'S EXPANSION FORMULA





Leetsch C.Hsu Peter J.S.Shiue《分析论及其应用》,2005年第21卷第4期


We present a constructive generalization of AbelGontscharoff's series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.

2.

Bivariate Blending ThieleWerner＇s Osculatory Rational Interpolation





Shuo Tang Yan Liang《高等学校计算数学学报(英文版)》,2007年第16卷第3期


Both the expansive Newton＇s interpolating polynomial and the ThieleWerner＇s interpolation are used to construct a kind of bivariate blending ThieleWerner＇s osculatory rational interpolation. A recursive algorithm and its characteristic properties are given. An error estimation is obtained and a numerical example is illustrated.

3.

Block based Newtonlike blending osculatory rational interpolation





Shuo Tang Le Zou Chensheng Li《分析论及其应用》,2010年第26卷第3期


With Newton’s interpolating formula, we construct a kind of block based Newtonlike blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the expansive Newton’s polynomial interpolation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.

4.

二元混合连分式展开的混合差商极限方法 被引次数：1





赵前进 檀结庆《东北数学》,2006年第22卷第4期


For a univariate function given by its Taylor series expansion,a continuedfraction expansion can be obtained with the Viscovatov's algorithm,as the limitingvalue of a Thiele interpolating continued fraction or by means of the determinantalformulas for inverse and reciprocal differences with coincident data points.In thispaper,both Viscovatovlike algorithms and Taylorlike expansions are incorporatedto yield bivariate blending continued expansions which are computed as the limitingvalue of bivariate blending rational interpolants,which are constructed based on symmetric blending differences.Numerical examples are given to show the effectivenessof our methods.

5.

Bivariate Blending ThieleWerner's Osculatory Rational Interpolation





Shuo Tang Yan Liang 《高等学校计算数学学报(英文版)》,2007年第16卷第3期


Both the expansive Newton's interpolating polynomial and the ThieleWerner's in terpolation are used to construct a kind of bivariate blending ThieleWerner's oscula tory rational interpolation.A recursive algorithm and its characteristic properties are given.An error estimation is obtained and a numerical example is illustrated.

6.

BLOCK BASED NEWTONLIKE BLENDING OSCULATORY RATIONAL INTERPOLATION





Shuo Tang Le Zou Chensheng Li《逼近论及其应用》,2010年第3期


With Newton＇s interpolating formula, we construct a kind of block based Newtonlike blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the expansive Newton＇s polynomial inter polation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.

7.

一种新形式的二元混合有理插值(英文)





邹乐 唐烁《数学季刊》,2011年第2期


Newton＇s polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of bivariate blending rational interpolants.Characteristic theorem is discussed.We give some new blending interpolation formulae.

8.

EQ 1 rot nonconforming finite element method for nonlinear dual phase lagging heat conduction equations





Yanmin Zhao Fenling Wang Dongyang Shi《应用数学学报(英文版)》,2013年第29卷第1期


EQ rot 1 nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semidiscrete and fullydiscrete schemes. By use of a special property, that is, the consistency error of this element is of order O(h2 ) one order higher than its interpolation error O(h), the superclose results of order O(h2 ) in broken H1 norm are obtained. At the same time, the global superconvergence in broken H1 norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h4 ) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ rot 1 element. Finally, optimal error estimate is gained for a proposed fullydiscrete scheme by different approaches from the previous literature.

9.

HAAR EXPANSIONS OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR LOGICAL DERIVATIVES





《分析论及其应用》,1993年第4期


In this paper,we study a special class of fractal interpolation functions,and give theirHaarwavelet expansions.On the basis of the expansions,we investigate the H(o¨)ldersmoothness of such functions and their logical derivatives of order α.

10.

球面上的Lagrange插值





周恒 王仁宏《东北数学》,2006年第22卷第2期


In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of total degree n.

11.

修正的 ThieleWerner型有理插值 被引次数：1





李昌文 朱晓临 邹乐《数学研究与评论》,2010年第30卷第4期


Through adjusting the order of interpolation nodes, we gave a kind of modified ThieleWerner rational interpolation. This interpolation method not only avoids the infinite value of inverse differences in constructing the Thiele continued fraction interpolation, but also simplifies the interpolating polynomial coefficients with constant coefficients in the ThieleWerner rational interpolation. Unattainable points and determinantal expression for this interpolation are considered. As an extension, some bivariate analogy is also discussed and numerical examples are given to show the validness of this method.

12.

C^1 C^2 INTERPOLATION OF SCATTERED DATA POINTS





WANGJIAYE ZHANGCAIMING《高校应用数学学报(英文版)》,1994年第9卷第1期


In this paper an error in [4] is pointed out and a method for constructing surface interpolating scattered data points is presented, The main feature of the method in this paper is that the surface so constructed is polynomial, which makes the construction simple and the calculation easy.

13.

样条型矩阵有理插值





杨松林《高等学校计算数学学报》,2005年第27卷第1期


The matrix valued rational interpolation is very useful in the partial realization problem and model reduction for all the linear system theory. Lagrange basic functions have been used in matrix valued rational interpolation. In this paper, according to the property of cardinal spline interpolation, we constructed a kind of spline type matrix valued rational interpolation, which based on cardinal spline. This spline type interpolation can avoid instability of high order polynomial interpolation and we obtained a useful formula.

14.

A robust method for inverse halftoning via twodimensional nonlinear pyramid





Yueping Kong Ping Zeng《中国光学快报(英文版)》,2007年第5卷第10期


Based on the principle of spatial pyramid for signal, a multiscale transform of twodimensional (2D) interpolating pyramid is constructed by the nonlinear median operator.

15.

BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS 被引次数：1





Xiaoyuan Qian 《计算数学(英文版)》,2002年第4期


AbstractNontensor product bivariate fractal interpolation functions defined on gridded rectangular domains are constructed. Linear spaces consisting of these functions are introduced. The relevant Lagrange interpolation problem is discussed. A negative result about the existence of affine fractal interpolation functions defined on such domains is obtained.

16.

The Nonexistence of Expansive Z^d Actions on Graphs 被引次数：1





En Hui SHI Li Zhen ZHOU《数学学报(英文版)》,2005年第21卷第6期


It is well known that if X is an arc or a circle, then there is no expansive homeomorphism on X. In this paper we prove that there is no expansive Z^d action on X, which answers the two questions raised by us before, In 1979, Mané proved that there is no expansive homeomorphism on infinite dimensional spaces. Contrary to this result, we construct an expansive Z^2 action on an infinite dimensional space. We also construct an expansive Z^2 action on a zero dimensional space but no element in Z^2 is expansive.

17.

Block Based Bivariate Blending Rational Interpolation via Symmetric Branched Continued Fractions





Qianjin Zhao Jieqing Tan《高等学校计算数学学报(英文版)》,2007年第16卷第1期


This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.

18.

Accuracy Analysis of the Adini Element for Biharmonic Equation





PingLUO QunLIN《数学学报(英文版)》,2004年第20卷第1期


In this paper,we consider the solution of the biharmonic equation using Adini nonconforming finite element,and report new results of the asympiotic error expansions of the interpolation error functionals and nonconforming remainder.These expansions are used to develop two extrapolation formulas and a series of sharp error estimates.Finally,the numerical results have verified the extrapolation theory.

19.

SOME BLENDING INTERPOLATION METHODS IN CAGD





罗钟铉 苏志勋《高等学校计算数学学报(英文版)》,1993年第2期


Some of the blending interpolation methods (which) stated by a convex combination technique are presented. This includes C1 ,C2 blending triangular interpolanls and C1 blending quadrilateral inter polanls for surfaces. The mentioned methods can be generalized to the construction of C" blending interpolants.

20.

Note on Rational Interpolants 被引次数：1





Tan Jieqing 《大学数学》,1993年第3期


<正> In this note we present a constructive proof of symmetrical determinantal formulas forthe numerator and denominator of an ordinary rational interpolant,consider the confluencecase and give new determinantal formulas of the rational interpolant by means of Lagrange'sbasis functions.
