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1.
插值算子逼近是逼近论中一个非常有趣的问题,尤其是以一些特殊的点为结点的插值算子的逼近问题很受人们的关注.研究了以第一类Chebyshev多项式零点为插值结点的Hermite插值算子在Orlicz范数下的逼近. 相似文献
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In order to relieve the deficiency of the usual cubic Hermite spline curves, the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic Hermite spline curves are given. And the characteristics of the quartic Hermite spline curves are discussed. The quartic Hermite spline curves not only have the same interpolation and conti-nuity properties of the usual cubic Hermite spline curves, but also can achieve local or global shape adjustment and C2 continuity by the shape parameters when the interpolation conditions are fixed. 相似文献
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在L_ω~p空间中引入了一种 K-泛函并由此建立了一种以第一类 Chebyshev多项式的零点为结点的三种修正高阶 Hermite-Fejer插值多项式及一种修正的高阶 Hermite插值多项式在L_ω~p空间中逼近的正逆定理. 文中的结果说明,对于这几种修正高阶多项式插值的逼近问题而言,正定理的解决意味着逆定理的解决. 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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在LPW空间中引入了一种K-泛函并由此建立了一种以第一类Chebyshev多项式的零点为结点的三种修正高阶Hermite-Fejer插值多项式及一种修正的高阶Hermite插值多项式在LPW空间中逼近的正逆定理.文中的结果说明,对于这几种修正高阶多项式插值的逼近问题而言,正定理的解决意味着逆定理的解决. 相似文献
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The present paper investigates the convergence of Hermite interpolation operators on the real line. The main result is: Given 0 〈 δo 〈 1/2, 0 〈 εo 〈 1. Let f ∈ C(-∞,∞) satisfy |y|= O(e^(1/2-δo)xk^2,) and |f(x)|t= O(e^(1-εo )x2^). Then for any given point x ∈ R, we have limn→Hn,(f, x) = f(x). 相似文献
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Hermite interpolation is a very important tool in approximation theory and numerical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermite interpolant is unique for a prescribed data set,and hence lacks freedom for the choice of an interpolating curve, which is a crucial requirement in design environment. Even though there is a rather well developed fractal theory for Hermite interpolation that offers a large flexibility in the choice of interpolants, it also has the shortcoming that the functions that can be well approximated are highly restricted to the class of self-affine functions. The primary objective of this paper is to suggest a C1-cubic Hermite interpolation scheme using a fractal methodology, namely, the coalescence hidden variable fractal interpolation, which works equally well for the approximation of a self-affine and non-self-affine data generating functions. The uniform error bound for the proposed fractal interpolant is established to demonstrate that the convergence properties are similar to that of the classical Hermite interpolant. For the Hermite interpolation problem, if the derivative values are not actually prescribed at the knots, then we assign these values so that the interpolant gains global C2-continuity. Consequently, the procedure culminates with the construction of cubic spline coalescence hidden variable fractal interpolants. Thus, the present article also provides an alternative to the construction of cubic spline coalescence hidden variable fractal interpolation functions through moments proposed by Chand and Kapoor [Fractals, 15(1)(2007), pp. 41-53]. 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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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
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For the approximation in $L_p$-norm, we determine the weakly asymptotic
orders for the simultaneous approximation errors of Sobolev classes by piecewise cubic Hermite interpolation with equidistant knots. For $p = 1$, $∞$, we obtain its values.
By these results we know that for the Sobolev classes, the approximation errors by
piecewise cubic Hermite interpolation are weakly equivalent to the corresponding
infinite-dimensional Kolmogorov widths. At the same time, the approximation errors of derivatives are weakly equivalent to the corresponding infinite-dimensional
Kolmogorov widths. 相似文献
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In this paper, planar parametric Hermite cubic interpolants with small curvature variation are studied. By minimization of an appropriate approximate functional, it is shown that a unique solution of the interpolation problem exists, and has a nice geometric interpretation. The best solution of such a problem is a quadratic geometric interpolant. The optimal approximation order 4 of the solution is confirmed. The approach is combined with strain energy minimization in order to obtain G1 cubic interpolatory spline. 相似文献
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给出一种基于商的形式的Lagrange与Hermite插值公式及其证明,同时还给出了两个相关的不等式. 相似文献
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Tian Xiao He 《Journal of Computational Analysis and Applications》2003,5(1):103-118
Multivariate rational exponential Lagrange interpolation formulas, Hermite interpolation formulas, and Hermite–Fejér interpolation formulas of the Newton type are established by using Carlitz's inversion formulas. The recurrence relation for constructing Lagrange interpolation is also given. In addition, by setting q1 in the obtained formulas, we obtain the corresponding polynomial interpolation formulas with combinatorial form. 相似文献
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We obtain the Laurent polynomial of Hermite interpolation on the unit circle for nodal systems more general than those formed by the n-roots of complex numbers with modulus one. Under suitable assumptions for the nodal system, that is, when it is constituted by the zeros of para-orthogonal polynomials with respect to appropriate measures or when it satisfies certain properties, we prove the convergence of the polynomial of Hermite-Fejér interpolation for continuous functions. Moreover, we also study the general Hermite interpolation problem on the unit circle and we obtain a sufficient condition on the interpolation conditions for the derivatives, in order to have uniform convergence for continuous functions.Finally, we obtain some improvements on the Hermite interpolation problems on the interval and for the Hermite trigonometric interpolation. 相似文献
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W.F. Florez C.A. BustamanteM. Giraldo A.F. Hill 《Applied mathematics and computation》2012,218(11):6446-6457
This paper presents a local Hermite radial basis function interpolation scheme for the velocity and pressure fields. The interpolation for velocity satisfies the continuity equation (mass conservative interpolation) while the pressure interpolation obeys the pressure equation. Additionally, the Dual Reciprocity Boundary Element method (DRBEM) is applied to obtain an integral representation of the Navier-Stokes equations. Then, the proposed local interpolation is used to obtain the values of the field variables and their partial derivatives at the boundary of the sub-domains. This interpolation allows one to obtain the boundary values needed for the integral formulas for velocity and pressure at some nodes within the sub-domains. In the proposed approach the boundary elements are merely used to parameterize the geometry, but not for the evaluation of the integrals as it is usually done. The presented multi-domain approach is different from the traditional ones in boundary elements because the resulting integral equations are non singular and the boundary data needed for the boundary integrals are approximated using a local interpolation. Some accurate results for simple Stokes problems and for the Navier-Stokes equations at low Reynolds numbers up to Re = 400 were obtained. 相似文献
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《Numerical Methods for Partial Differential Equations》2018,34(3):959-981
In this article, integrated radial basis functions (IRBFs) are used for Hermite interpolation in the solution of differential equations, resulting in a new meshless symmetric RBF method. Both global and local approximation‐based schemes are derived. For the latter, the focus is on the construction of compact approximation stencils, where a sparse system matrix and a high‐order accuracy can be achieved together. Cartesian‐grid‐based stencils are possible for problems defined on nonrectangular domains. Furthermore, the effects of the RBF width on the solution accuracy for a given grid size are fully explored with a reasonable computational cost. The proposed schemes are numerically verified in some elliptic boundary‐value problems governed by the Poisson and convection‐diffusion equations. High levels of the solution accuracy are obtained using relatively coarse discretisations. 相似文献
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基于函数空间{1,sint,cost,sin~2t,sin~3t,cos~3t}构造了一种形状可调的三次三角Hermite插值样条.该样条不仅具有带参数的Hermite型插值样条的主要特性,而且在插值节点为等距时可自动满足C2连续,其形状还可通过所带的参数进行调节.在适当条件下,该样条对应的Ferguson曲线可精确表示工程中一些常见的曲线. 相似文献
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本文研究了具调节因子的Hermite函数的拟谱方法在赋权Sobolev空间中函数的逼近.通过具调节因子的Hermite多项式的性质和相应的Gauss类型的求积公式,得到了在具调节因子的Hermite多项式的零点上的插值算子的稳定性以及误差界.并具有通常的高阶收敛性. 相似文献