共查询到18条相似文献,搜索用时 187 毫秒
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1引 言
单位球面上的插值问题一直是三元插值问题中比较受关注的部分.近年来,球面上的 Lagrange插值问题已经得到了很好地解决.例如[1]中给出了构造单位球面上的Lagrange 插值适定结点组的一种方法:添加圆周法.[2]和[3]中研究了单位球面上的多项式插值问题,给出了构造单位球面上的插值适定结点组的另外两种方法. 相似文献
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对多元多项式分次插值适定结点组的构造理论进行了深入的研究与探讨.在沿无重复分量代数曲线进行Lagrange插值的基础上,给出了沿无重复分量分次代数曲线进行分次Lagrane插值的方法,并利用这一结果进一步给出了在R~2上构造分次Lagrange插值适定结点组的基本方法.另外,利用弱Gr(o|¨)bner基这一新的数学概念,以及构造平面代数曲线上插值适定结点组的理论,进一步给出了构造平面分次代数曲线上分次插值适定结点组的方法,从而基本上弄清了多元分次Lagrange插值适定结点组的几何结构和基本特征. 相似文献
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广义Vandermonde行列式及其应用 总被引:15,自引:7,他引:8
1 广义Vandermonde行列式的定义 1966年,I.J.Schoenberg在文[1]中明确提出具有一般性的Hermite-Birkhoff插值及其插值适定性问题.而一般的Hermite-Birkhoff插值问题则未必是适定的,关于这方面目前已有许多工作,见[2]—[7].我们知道,Hermite-Birkhoff插值问题是 Hermite插值问题的推 相似文献
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本文对于一般的Hermite插值算子的多元扩张算子,给出了线性独立的插值泛函组及相应的Lagrange基本多项式。 相似文献
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本文研究在单位圆周{|z| =1}上一致逼近函数f(z)及其导数,利用Hermite插值中的基函数建立复有理型插值,并证明它们在{|z| =1}上分别一致收敛于f(z)或f′(z) ,给出了收敛速度. 相似文献
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二元样条函数插值在计算几何与计算机辅助几何设计中有着重要的作用.本文给出了一种矩形剖分上二元线性样条函数进行Lagrange插值时插值适定结点组所满足的拓扑与几何性质,这种性质依赖于二元线性样条函数所决定的分片线性代数曲线. 相似文献
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Ming Zhang 《Applied Numerical Mathematics》2011,61(5):666-674
The purpose of this paper is to put forward a kind of Hermite interpolation scheme on the unit sphere. We prove the superposition interpolation process for Hermite interpolation on the sphere and give some examples of interpolation schemes. The numerical examples shows that this method for Hermite interpolation on the sphere is feasible. And this paper can be regarded as an extension and a development of Lagrange interpolation on the sphere since it includes Lagrange interpolation as a particular case. 相似文献
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Lagrange Interpolation on a Sphere 总被引:1,自引:0,他引:1
§ 1.Introduction LetnbeanonnegativeintegerandS ={(x ,y ,z)∈R3 |x2 + y2 +z2 =1 }betheunitsphereinR3 .P( 2 )n andP( 3 )n denotethespaceofallbivariatepolynomialsoftotaldegree≤nandthespaceofalltrivariatepolynomialsoftotaldegree≤nrespectively ,i.e .P( 2 )n =∑0≤i+j≤naijxiyj|aij ∈R ,P( 3 … 相似文献
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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. 相似文献
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In this paper, we prove convergence rates for spherical spline Hermite interpolation on the sphere Sd−1 via an error estimate given in a technical report by Luo and Levesley. The functionals in the Hermite interpolation are either point evaluations of pseudodifferential operators or rotational differential operators, the desirable feature of these operators being that they map polynomials to polynomials. Convergence rates for certain derivatives are given in terms of maximum point separation. 相似文献
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修正的 Thiele-Werner型有理插值 总被引:1,自引:0,他引:1
Through adjusting the order of interpolation nodes, we gave a kind of modified Thiele-Werner 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 Thiele-Werner 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. 相似文献
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The multivariate interpolating (m, l, s)-splines are a natural generalization of Duchon's thin plate splines (TPS). More precisely, we consider the problem of interpolation with respect to some finite number of linear continuous functionals defined on a semi-Hilbert space and minimizing its semi-norm. The (m, l, s)-splines are explicitly given as a linear combination of translates of radial basis functions. We prove the existence and uniqueness of the interpolating (m, l, s)-splines and investigate some of their properties. Finally, we present some practical examples of (m, l, s)-splines for Lagrange and Hermite interpolation. 相似文献
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Ana C. Matos 《Numerical Algorithms》1996,11(1):255-269
The aim of this paper is to give some convergence results for some sequences of generalized Padé-type approximants. We will consider two types of interpolatory functionals: one corresponding to Langrange and Hermite interpolation and the other corresponding to orthogonal expansions. For these two cases we will give sufficient conditions on the generating functionG(x, t) and on the linear functionalc in order to obtain the convergence of the corresponding sequence of generalized Padé-type approximants. Some examples are given. 相似文献
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With Newton’s interpolating formula, we construct a kind of block based Newton-like 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. 相似文献