共查询到20条相似文献,搜索用时 593 毫秒
1.
Shuo Tang Yan Liang 《高等学校计算数学学报(英文版)》2007,16(3):271-288
Both the expansive Newton's interpolating polynomial and the Thiele-Werner's interpolation are used to construct a kind of bivariate blending Thiele-Werner's osculatory rational interpolation. A recursive algorithm and its characteristic properties are given. An error estimation is obtained and a numerical example is illustrated. 相似文献
2.
3.
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
4.
This is the third part of a note on multivariate interpolation. Some remainder formulas for interpolation on knot sets that are perspective images of standard lower data sets are given. They apply to all knot systems considered in parts I and II.Partially supported by PS900121. 相似文献
5.
Y. G. Zhang 《分析论及其应用》2016,32(1):65-77
General interpolation formulae for barycentric interpolation and barycentric rational Hermite interpolation are established by introducing multiple parameters,which include many kinds of barycentric interpolation and barycentric rational Hermite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method. 相似文献
6.
Lacunary Interpolation by Antiperiodic Trigonometric Polynomials 总被引:17,自引:0,他引:17
The problem of lacunary trigonometric interpolation is investigated. Does a trigonometric polynomial T exist which satisfies T(x
k) = a
k, D
m
T(x
k) = b
k, 0 k n – 1, where x
k = k/n is a nodal set, a
k and b
k are prescribed complex numbers,
and m N. Results obtained by several authors for the periodic case are extended to the antiperiodic case. In particular solvability is established when n as well as m are even. In this case a periodic solution does not exist. 相似文献
7.
Suppose that (X 0, X 1) is a Banach couple, X 0 ∩ X 1 is dense in X 0 and X 1, (X0,X1)θq (0 < θ < 1, 1 ≤ q < ∞) are the spaces of the real interpolation method, ψ ∈ (X 0 ∩ X 1), ψ ≠ 0, is a linear functional, N = Ker ψ, and N i stands for N with the norm inherited from X i (i = 0, 1). The following theorem is proved: the norms of the spaces (N0,N1)θ,q and (X0,X1)θ,q are equivalent on N if and only if θ ? (0, α) ∪ (β∞, α0 ∪ (β0, α∞) ∪ (β, 1), where α, β, α0, β0, α∞, and β ∞ are the dilation indices of the function k(t)=K(t,ψ;X 0 * ,X 1 * ). 相似文献
8.
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
9.
二元有理插值的迭加算法 总被引:1,自引:1,他引:0
在已有基础上给出一种新的算法,即迭加插值算法,并给出相应的插值有理函数的具体表达式,以及与已有算法比较,该算法具有较大的灵活性,更便于实际应用. 相似文献
10.
In this paper, we consider the bivariate Hermite interpolation introduced by Bojanov and Xu [SIAM J. Numer. Anal. 39(5) (2002) 1780–1793]. The nodes of the interpolation with Π2k-δ, where δ=0 or 1, are the intersection points of 2k+1 distinct rays from the origin with a multiset of k+1-δ concentric circles. Parameters are the values and successive radial derivatives, whenever the corresponding circle is multiple. The poisedness of this interpolation was proved only for the set of equidistant rays [Bojanov and Xu, 2002] and its counterparts with other conic sections [Hakopian and Ismail, East J. Approx. 9 (2003) 251–267]. We show that the poisedness of this (k+1-δ)(2k+1) dimensional Hermite interpolation problem is equivalent to the poisedness of certain 2k+1 dimensional Lagrange interpolation problems. Then the poisedness of Bojanov–Xu interpolation for a wide family of sets of rays satisfying some simple conditions is established. Our results hold also with above circles replaced by ellipses, hyperbolas, and pairs of parallel lines.Next a conjecture [Hakopian and Ismail, J. Approx. Theory 116 (2002) 76–99] concerning a poisedness relation between the Bojanov–Xu interpolation, with set of rays symmetric about x-axis, and certain univariate lacunary interpolations is established. At the end the poisedness for a wide class of lacunary interpolations is obtained. 相似文献
11.
12.
心磁图是根据人体心脏跳动产生的微弱磁场测量信号计算得到的医学图像,它较心电图诊断心脏疾病具有更高的灵敏度和准确性.为了提高心磁图的成像精度,通常需要对心磁检测数据进行插值处理.提供了双立方插值和二元三次样条插值两种插值方法,应用实例的结果表明,三次样条插值的效果比双立方插值效果好,基本能达到应用的要求. 相似文献
13.
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
14.
15.
Jian-Kang Zhang Timothy N. Davidson Zhi-Quan Luo K. Max Wong 《Applied and Computational Harmonic Analysis》2001,11(3):892
In this paper we characterize all totally interpolating biorthogonal finite impulse response (FIR) multifilter banks of multiplicity two, and provide a design framework for corresponding compactly supported multiwavelet systems with high approximation order. In these systems, each component of the analysis and synthesis portions possesses the interpolating property. The design framework is based on scalar filter banks, and examples with approximation order two and three are provided. We show that our multiwavelet systems preserve almost all of the desirable properties of the generalized interpolating scalar wavelet systems, including the dyadic-rational nature of the filter coefficients, equality of the flatness degree of the low-pass filters and the approximation order of the corresponding functions, and equality between the uniform samples of a signal and its projection coefficients for a given scale. This last property allows us to avoid the cumbersome prefiltering associated with standard multiwavelet systems. We also show that there are no symmetric totally interpolating biorthogonal multifilter banks of multiplicity two. Finally, we point out that our design framework incorporates a simple relationship between the multiscaling functions and multiwavelets that substantially simplifies the implementation of the system. 相似文献
16.
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
17.
A construction method of Fractal Interpolation Surfaces on a rectangular domain with arbitrary interpolation nodes is introduced. The variation properties of the binary functions corresponding to this type of fractal interpolation surfaces are discussed. Based on the relationship between Box-counting dimension and variation, some results about Box-counting dimension of the fractal interpolation surfaces are given. 相似文献
18.
Ying-guang Shi 《计算数学(英文版)》2001,19(2):151-156
1. IntroductionThis note deals with convergence of (0,1,2,3) illterpolation on an arbitrary system of nodes.Fisrt we illtroduce some definitions and notations.LetGiven a fiXed even integer m, let Ajk 6 Pm.--1 (the set of polynomials of degree at most mn-- 1)satisfyThen the (0,1,...,m--1) Hermite--Fej6r type illterpolation for f 6 C[--1, 1] is defined byand the (0,1,...,m--1) Hernilte interpolation for f e Cd--'[--1, 1] is defined by(of. [6]). We also need a well known fact:where 11' 11 sta… 相似文献
19.
Polynomial interpolation of two variables based on points that are located on multiple circles is studied. First, the poisedness of a Birkhoff interpolation on points that are located on several concentric circles is established. Second, using a factorization method, the poisedness of a Hermite interpolation based on points located on various circles, not necessarily concentric, is established. Even in the case of Lagrange interpolation, this gives many new sets of poised interpolation points. 相似文献