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41.
利用三次非均匀有理B样条,给出了一种构造局部插值曲线的方法,生成的插值曲线是C2连续的.曲线表示式中带有一个局部形状参数,随着一个局部形状参数值的增大,所给曲线将局部地接近插值点构成的控制多边形.基于三次非均匀有理B样条函数的局部单调性和一种保单调性的准则,给出了所给插值曲线的保单调性的条件. 相似文献
42.
This short note presents four examples of compactly supported symmetric refinable componentwise polynomial functions: (i) a componentwise constant interpolatory continuous refinable function and its derived symmetric tight wavelet frame; (ii) a componentwise constant continuous orthonormal and interpolatory refinable function and its associated symmetric orthonormal wavelet basis; (iii) a differentiable symmetric componentwise linear polynomial orthonormal refinable function; (iv) a symmetric refinable componentwise linear polynomial which is interpolatory and differentiable. 相似文献
43.
María Álvarez de Morales Lidia Fernández Teresa E. Pérez Miguel A. Piñar 《Numerical Algorithms》2007,45(1-4):153-166
In this paper, we consider bivariate orthogonal polynomials associated with a quasi-definite moment functional which satisfies
a Pearson-type partial differential equation. For these polynomials differential properties are obtained. In particular, we
deduce some structure and orthogonality relations for the successive partial derivatives of the polynomials.
相似文献
44.
45.
Barry Booton 《Journal of Mathematical Analysis and Applications》2007,335(2):1416-1433
We apply tools of interpolation theory and a commutative property of the Hilbert transform to prove necessary and sufficient conditions related to trigonometric series. These results extend and improve related theorems proven by several authors, summarized by Boas. In addition, we explore inequalities and operators, both connected to Hardy's inequalities, on certain classes of functions, including quasimonotone functions. 相似文献
46.
Richard Cowan 《Annals of the Institute of Statistical Mathematics》1987,39(1):103-111
Summary In this paper a new bivariate exponential distribution, arising naturally in the theory of Poisson line processes, is studied.
The distribution has some interesting and useful properties which renders it suitable for use in statistical modelling work.
It is presented in the spirit of adding to the repertoire of bivariate exponential forms. It joins other models, such as those
of Downton (1970,J. R. Statist. Soc., B,32, 408–417), Marshall and Olkin (1967,J. Appl. Prob.,4, 291–302) and Nagao and Kadoya (1971,Bulletin of the Disaster Prevention Research Institute,20, 3, 183–215), which have their origins in the theory of stochastic processes. 相似文献
47.
Emanuele Galligani 《Annali dell'Universita di Ferrara》2002,48(1):99-117
Sunto L’applicazione di noti metodi che utilizzano funzioni di tipo blending per la costruzione di funzioni bivariate C1 per l’interpolazione di dati, richiede la conoscenza delle derivate parziali del primo ordine ai vertici di una triangolazione
sottostante. In questo lavoro consideriamo il metodo proposto da Nielson, che consiste nel calcolare stime delle derivate
parziali del primo ordine minimizzando un opportuno funzionale quadratico, caratterizzato da parametri di tensione non negativi.
Scopo del lavoro è l’analisi di alcune proprietà particolari di questo funzionale per la costruzione di algoritmi efficienti
e robusti per la determinazione delle stime suddette delle derivate quando si ha a che fare con insiemi di dati di grandi
dimensioni.
Abstract
The application of widely known blending methods for constructingC
1 bivariate functions interpolating scattered data requires the knowledge of the partial derivatives of first order at the
vertices of an underlying triangulation. In this paper we consider the method proposed by Nielson that consists in computing
estimates of the first order partial derivatives by minimizing an appropriate quadratic functional, characterized by nonnegative
tension parameters. The aim of the paper is to analyse some peculiar properties of this functional in order to construct robust
and efficient algorithms for determining the above estimates of the derivatives when we are concerned with extremely large
data sets.
相似文献
48.
空间理性八节点块体元 总被引:1,自引:0,他引:1
推导出空间八节点块体理性有限元列式,采用具有直到三次多项式的空间问题的微分方程的解作为插值的近似函数,数例结果表明空间理性八节点块体元的有效性。 相似文献
49.
D. D. Tcheutia M. Foupouagnigni Y. Guemo Tefo I. Area 《Journal of Difference Equations and Applications》2017,23(12):2004-2036
Partial divided-difference equations and three-term recurrence relations satisfied by the bivariate Askey–Wilson and the bivariate q-Racah polynomials are computed in this work. By using limiting processes, partial divided (or q)-difference equations and three-term recurrence relations are also provided for each of the following families of orthogonal polynomials: the bivariate continuous dual q-Hahn, the bivariate Al-Salam-Chihara, the bivariate continuous q-Hahn, the bivariate q-Hahn, the bivariate dual q-Hahn, the bivariate q-Krawtchouk, the bivariate q-Meixner, and the bivariate q-Charlier polynomials. 相似文献
50.
We establish various properties for the zero sets of three families of bivariate Hermite polynomials. Special emphasis is given to those bivariate orthogonal polynomials introduced by Hermite by means of a Rodrigues type formula related to a general positive definite quadratic form. For this family we prove that the zero set of the polynomial of total degree n+m consists of exactly n+m disjoint branches and possesses n+m asymptotes. A natural extension of the notion of interlacing is introduced and it is proved that the zero sets of the family under discussion obey this property. The results show that the properties of the zero sets, considered as affine algebraic curves in R2, are completely different for the three families analyzed. 相似文献