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1.
Tianxiao He Leetsch C. Hsu Peter J. S. Shiue 《分析论及其应用》2005,21(4):359-369
We present a constructive generalization of Abel-Gontscharoff'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. 相似文献
2.
In this paper, we consider the Straight Line Type Node Configuration C (SLTNCC) in multivariate polynomial interpolation as the result of different kinds of transformations of lines (such as parallel translations, rotations). Corresponding to these transformations we define different kinds of interpolation problems for the SLTNCC. The expression of the confluent multivariate Vandermonde determinant of the coefficient matrix for each of these interpolation problems is obtained, and from this expression we conclude the related interpolation problem is unisolvent. Also, we give a kind of generalization of the SLTNCC in Section 5. As well, we obtain an expression of the interpolating polynomial for a kind of interpolation problem discussed in this paper. 相似文献
3.
One of the problems in bivariate polynomial interpolation is the choice of a space of polynomials suitable for interpolating a given set of data. Depending on the number of data, a usual space is that of polynomials in 2 variables of total degree not greater than k. However, these spaces are not enough to cover many interpolation problems. Here, we are interested in spaces of polynomials of total degree not greater than k whose degree diminishes along some prescribed directions. These spaces arise naturally in some interpolation problems and we describe them in terms of polynomials satisfying some asymptotic interpolation conditions. This provides a general frame to the interpolation problems studied in some of our recent papers. 相似文献
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5.
1 IntroductionIn this paper,we letPn,… ,nsn′s( or Psn) be the ( s-variate) polynomial space of all real ( s-variate) polynomials with the degreeof each variate atmostn and use the usual multivariate notationwj =wj11 … wjss,| j| =j1 +… + js( j1 ,… ,js∈ Z+) .[1 ] and [2 ] have discussed the Cross Type Node Configuration ( CRTNC) and thecorresponding bivariate interpolation in R2 .In this paper,we considerRs={ ( w1 ,… ,ws) :wi ∈ R,i =1 ,… ,s} .We say that s( s-1 ) -dimensional h… 相似文献
6.
C. de Boor 《Advances in Computational Mathematics》2007,26(1-3):63-70
This is an extension and emendation of recent results on the use of Gauss elimination in multivariate polynomial interpolation
and, in particular, ideal interpolation.
Dedicated to Mariano Gasca on the occasion of his sixtieth birthday 相似文献
7.
Daniela Rosca. 《Mathematics of Computation》2005,74(252):1803-1829
In this paper we construct certain continuous piecewise rational wavelets on arbitrary spherical triangulations, giving explicit expressions of these wavelets. Our wavelets have small support, a fact which is very important in working with large amounts of data, since the algorithms for decomposition, compression and reconstruction deal with sparse matrices. We also give a quasi-interpolant associated to a given triangulation and study the approximation error. Some numerical examples are given to illustrate the efficiency of our wavelets.
8.
Carl Boor 《Advances in Computational Mathematics》2006,24(1-4):143-153
A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary
linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning interpolation by
radial polynomials. Schaback's interpolant is explored.
Happy 60th and beyond, Charlie!
Mathematics subject classifications (2000) 41A05, 41A6. 相似文献
9.
A kind of generalization of the Curve Type Node Configuration is given in this paper,and it is called the generalized node configuration CTNCB in RS(S>2).The related multivariate polynomial interpolation problem is discussed.It is proved that the CTNCB is an appropriate node configuration for the polynomial space PSn (S>2).And the expressions of the multivariate Vandermonde determinants that are related to the Odd Curve Type Node Configuration in R2 are also obtained. 相似文献
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11.
多项式空间的对偶及其在多元插值中的应用 总被引:1,自引:0,他引:1
本文通过把域K上n元多项式环看成域K上的无限维向量空间A,把n维仿射空间K^n中的每一点看成A上的线性泛函,从而K^n为对偶空间A^*的子集,利用对偶空间的理论得到了一些有趣的理论结果,弄清了K^n上点有限拓扑的结构,给出了判定给定结点组是否是给定多项式空间的适定结点组的判定准则,最后还给出了构造理想对偶基的一种算法。 相似文献
12.
《Annals of Pure and Applied Logic》2018,169(12):1369-1418
Proof-theoretic method has been successfully used almost from the inception of interpolation properties to provide efficient constructive proofs thereof. Until recently, the method was limited to sequent calculi (and their notational variants), despite the richness of generalizations of sequent structures developed in structural proof theory in the meantime. In this paper, we provide a systematic and uniform account of the recent extension of this proof-theoretic method to hypersequents, nested sequents, and labelled sequents for normal modal logic. The method is presented in terms and notation easily adaptable to other similar formalisms, and interpolant transformations are stated for typical rule types rather than for individual rules. 相似文献
13.
Piecewise polynomial,positive definite and compactly supported radial functions of minimal degree 总被引:23,自引:0,他引:23
Holger Wendland 《Advances in Computational Mathematics》1995,4(1):389-396
We construct a new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support. For given smoothness and space dimension it is proved that they are of minimal degree and unique up to a constant factor. Finally, we establish connections between already known functions of this kind. 相似文献
14.
Principal lattices are distributions of points in the plane obtained from a triangle by drawing equidistant parallel lines
to the sides and taking the intersection points as nodes. Interpolation on principal lattices leads to particularly simple
formulae. These sets were generalized by Lee and Phillips considering three-pencil lattices, generated by three linear pencils.
Inspired by the addition of points on cubic curves and using duality, we introduce an addition of lines as a way of constructing
lattices generated by cubic pencils. They include three-pencil lattices and then principal lattices. Interpolation on lattices
generated by cubic pencils has the same good properties and simple formulae as on principal lattices.
Dedicated to C.A. Micchelli for his mathematical contributions and friendship on occasion of his sixtieth birthday
Mathematics subject classifications (2000) 41A05, 41A63, 65D05.
J.M. Carnicer: Partially supported by the Spanish Research Grant BFM2003-03510, by Gobierno de Aragón and Fondo Social Europeo. 相似文献
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16.
Generalizing a classical idea of Biermann, we study a way of constructing a unisolvent array for Lagrange interpolation in Cn+m out of two suitably ordered unisolvent arrays respectively in Cn and Cm. For this new array, important objects of Lagrange interpolation theory (fundamental Lagrange polynomials, Newton polynomials, divided difference operator, vandermondian, etc.) are computed.
AMS subject classification 41A05, 41A63 相似文献
17.
In this paper we study a class of multivariate Hermite interpolation problem on 2~d nodes with dimension d ≥ 2 which can be seen as a generalization of two classical Hermite interpolation problems of d = 2. Two combinatorial identities are firstly given and then the regularity of the proposed interpolation problem is proved. 相似文献
18.
1 引言多元Lagrange插值一直是计算数学中一个重要的研究课题.为了解决一些实际科学计算问题(如多元函数的计算,曲面的外形设计和有限元格式的建立等),有关多元多项式插值的理论与方法的研究在近二、三十年中迅速发展起来.在研究多元多项式插值时, 一个首先必须解决的问题就是多元插值的适定性问题.目前,国内外对这一问题的研究大 相似文献
19.
Manuela Nees 《Advances in Computational Mathematics》1996,5(1):137-151
In this paper, we develop two algorithms for Chebyshev approximation of continuous functions on [0, 1]
n
using the modulus of continuity and the maximum norm estimated by a given finite data system. The algorithms are based on constructive versions of Kolmogorov's superposition theorem. One of the algorithms we apply to neural networks. 相似文献
20.
A. Le Méhauté 《Advances in Computational Mathematics》2000,12(4):311-333
The purpose of this paper is to present some aspects of multivariate Hermite polynomial interpolation. We do not focus on
algebraic considerations, combinatoric and geometric aspects, but on explicitation of formulas for uniform and non-uniform
bivariate interpolation and some higher dimensional problems. The concepts of similar and equivalent interpolation schemes
are introduced and some differential aspects related to them are also investigated.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献