共查询到20条相似文献,搜索用时 31 毫秒
1.
Anke Gresbrand 《Numerical Algorithms》1996,12(1):151-158
A recursion formula for rational B-splines with prescribed poles is given that reduces to DeBoor's recursion when all poles are at infinity. Some properties of polynomial B-splines generalize to these rational B-splines: partition of unity, a knot inserting algorithm, numerical stability. It can be proved that the rational B-splines are identical with the Chebyshevian B-splines constructed by T. Lyche. The recursions are not identical and the one for the rational B-splines is more convenient. Furthermore, the rational B-splines are identified as special NURBS. The weights can be chosen depending on the poles. 相似文献
2.
3.
4.
5.
Four-term recurrence relations with constant coefficients are derived for a wide class of T chebycheffian B-splines, LB-splines
and complex B-splines. Such a relation exists whenever the differential operator defining the underlying “polynomial” space
can be factored in two essentially different ways. The four lower order B-splines in the recurrence relation appear in two
pairs, each pair corresponding to one of these factorization. It is shown that the two-term recurrence relations for polynomial,
trigonometric and hyperbolic B-splines as well as other known two-term recurrence relations are obtained directly from the
four-term recurrence relations in a unified and systematic way. The above derivation also yields two different two-term recurrence
relations for Green’s functions of these “polynomial” spaces In this context the special examples of exponential functions
and rational functions are analyzed in detail. 相似文献
6.
7.
K. Mørken 《Constructive Approximation》1991,7(1):195-208
In this paper it is shown how the algebraic product of two spline functions, each represented in terms of B-splines, can again be represented as a linear combination of suitable B-splines. As a corollary to this result we obtain an explicit representation of a given B-spline function in terms of B-splines of some arbitrary higher degree. This generalizes some known results for raising the degree by one. Recurrence relations for both products and degree raising are established that may be useful for computation.Communicated by Larry L. Schumaker. 相似文献
8.
二元三方向剖分中B样条的B网结构与递推算法 总被引:2,自引:0,他引:2
§1.引言众所周知,de Boor-Con递推公式及微分-差分公式对于一元B样条的理论和应用极为重要。在多元样条中是否存在类似的结果,已成为近年来的研究课题。本文从B网结构出发,讨论三向剖分下不同次数样条空间的B样条之间的递推关系,指出不能简单地把函数形式的de Boor-Con公式搬到这里,然而可以在B网意义下实现递推。与一 相似文献
9.
In this paper we study B-splines when the intervals between consecutive knots are in geometric progression and obtain generalizations of the particularly simple properties of the uniform B-splines, where the knots are equally spaced. 相似文献
10.
1引言 B样条在计算机图形学和几何建模等领域有着广泛的应用[3,8].在应用过程中,通常都需要对得到的模型进行修改以到达更好的效果.对于B样条曲线,利用节点插入算法可以有效地进行局部修改. 相似文献
11.
In this paper, we are concerned with biorthogonal Wilson bases having B-splines as well as powers of sinc functions as window
functions. We prove properties of B-splines and exponential Euler splines and use these properties to estimate the Riesz bounds
of the Wilson bases. 相似文献
12.
§1.引言 自七十年代末,高维B-样条的理论和方法,发展极为迅速.Micchelli建立了高维均差概念,用线性泛函作工具,重新给出高维B-样条的定义,并将一维B-样条两个主要递推公式推广到高维.随后,Dahmen从微分方程基本解、Hakopian用积分演算公式 相似文献
13.
Christophe Rabut 《Numerical Algorithms》2005,39(1-3):329-348
We present in this paper a family of functions which are tensor product functions in subdomains, while not having the usual drawback of functions which are tensor product functions in the whole domain. With these functions we can add more points in some region without adding points on lines parallel to the axes. These functions are linear combinations of tensor product polynomial B-splines, and the knots of different B-splines are less connected together than with usual polynomial B-splines. Approximation of functions, or data, with such functions gives satisfactory results, as shown by numerical experimentation.
AMS subject classification 41A15, 41A63, 65Dxx 相似文献
14.
《Applied and Computational Harmonic Analysis》2000,8(1):24-31
We present a construction of a refinable compactly supported vector of functions which is biorthogonal to the vector of B-splines of a given degree with multiple knots at the integers with prescribed multiplicity. The construction is based on Hermite interpolatory subdivision schemes, and on the relation between B-splines and divided differences. The biorthogonal vector of functions is shown to be refinable, with a mask related to that of the Hermite scheme. For simplicity of presentation the special (scalar) case, corresponding to B-splines with simple knots, is treated separately. 相似文献
15.
Edward Neuman 《Journal of Computational and Applied Mathematics》1981,7(1):51-62
The problem of determining the moments and the Fourier transforms of B-splines with arbitrary knots is considered. There exists a simple connection between the moments of such splines and the so-called extended Stirling numbers of the second kind which are defined in section 2. Some recurrence relations for the moments of B-splines with arbitrary knots are given in section 3. In the case of equidistant knots we have also further recurrences. For the forward, central and perfect B-splines the explicit formulas for the moments are given in section 3. The Fourier transforms of B-splines is treated in section 4. The final section is devoted to so-called Stieltjes series connected with the nonnegative weight function w(x) and such that in some closed interval [a, b]. It is proved that such series for the particular values of the independent variable may be expressed by the finite sums which contain the nodes and coefficients of the optimal (in the Davies sense) quadrature formulas. 相似文献
16.
In this paper an efficient estimation methodology for the partially linear models with random effects is proposed. For this, we use the generalized least square estimate (GLSE) and the B-splines methods to estimate the unknowns, and employ the penalized least square method to obtain the estimators of the random effects item. Further, we also consider the estimation for the variance components. Compared with the existing methods, our proposed methodology performs well. The asymptotic properties of the estimators are obtained. A simulation study is carried out to assess the performance of our proposed methodology. 相似文献
17.
Gerlind Plonka 《Advances in Computational Mathematics》1995,3(1):1-22
The Fourier transforms of B-splines with multiple integer knots are shown to satisfy a simple recursion relation. This recursion
formula is applied to derive a generalized two-scale relation for B-splines with multiple knots. Furthermore, the structure
of the corresponding autocorrelation symbol is investigated.
In particular, it can be observed that the solvability of the cardinal Hermite spline interpolation problem for spline functions
of degree 2m+1 and defectr, first considered by Lipow and Schoenberg [9], is equivalent to the Riesz basis property of our B-splines with degreem and defectr. In this way we obtain a new, simple proof for the assertion that the cardinal Hermite spline interpolation problem in [9]
has a unique solution. 相似文献
18.
Gerlind Plonka 《Advances in Computational Mathematics》1995,3(1-2):1-22
The Fourier transforms of B-splines with multiple integer knots are shown to satisfy a simple recursion relation. This recursion formula is applied to derive a generalized two-scale relation for B-splines with multiple knots. Furthermore, the structure of the corresponding autocorrelation symbol is investigated. In particular, it can be observed that the solvability of the cardinal Hermite spline interpolation problem for spline functions of degree 2m+1 and defectr, first considered by Lipow and Schoenberg [9], is equivalent to the Riesz basis property of our B-splines with degreem and defectr. In this way we obtain a new, simple proof for the assertion that the cardinal Hermite spline interpolation problem in [9] has a unique solution. 相似文献
19.
Complex B-splines as introduced in Forster et al. (Appl. Comput. Harmon. Anal. 20:281–282, 2006) are an extension of Schoenberg’s cardinal splines to include complex orders. We exhibit relationships between these complex
B-splines and the complex analogues of the classical difference and divided difference operators and prove a generalization
of the Hermite–Genocchi formula. This generalized Hermite–Genocchi formula then gives rise to a more general class of complex
B-splines that allows for some interesting stochastic interpretations.
相似文献
20.
Klaus Höllig Christian Apprich Anja Streit 《Advances in Computational Mathematics》2005,23(1-2):215-237
The Web-method is a meshless finite element technique which uses weighted extended B-splines (Web-splines) on a tensor product grid as basis functions. It combines the computational advantages of B-splines and standard mesh-based elements. In particular, degree and smoothness can be chosen arbitrarily without substantially increasing the dimension. Hence, accurate approximations are obtained with relatively few parameters. Moreover, the regular grid is well suited for hierarchical refinement and multigrid techniques. This article should serve as an introduction to finite element approximation with B-splines. We first review the construction of Web-bases and discuss their basic properties. Then we illustrate the performance of Ritz–Galerkin schemes for a model problem and applications in linear elasticity. Finally, we discuss several implementation aspects.
AMS subject classification 65N30, 41A15, 74S05Anja Streit: Present address: Fraunhofer ITWM, 67663 Kaiserslautern, Germany. 相似文献