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1.
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
2.
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
3.
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
4.
We present formulas for the divided differences of the remainder of the interpolation polynomial that include some recent interesting formulas as special cases. 相似文献
5.
Xing-hua WANG Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2007,50(11):1651-1660
Explicit representations for the Hermite interpolation and their derivatives of any order are provided.Furthermore,suppose that the interpolated function f has continuous derivatives of sufficiently high order on some sufficiently small neighborhood of a given point x and any group of nodes are also given on the neighborhood.If the derivatives of any order of the Hermite interpolation polynomial of f at the point x are applied to approximating the corresponding derivatives of the function f(x),the asymptotic representations for the remainder are presented. 相似文献
6.
7.
A. G. García M. A. Hernndez-Medina 《Journal of Mathematical Analysis and Applications》2003,280(2):221-231
The close relationship between discrete Sturm–Liouville problems belonging to the so-called limit-circle case, the indeterminate Hamburger moment problem and the search of self-adjoint extensions of the associated semi-infinite Jacobi matrix is well known. In this paper, all these important topics are also related with associated sampling expansions involving analytic Lagrange-type interpolation series. 相似文献
8.
Geometry of interpolation sets in derivative free optimization 总被引:2,自引:0,他引:2
We consider derivative free methods based on sampling approaches for nonlinear optimization problems where derivatives of the objective function are not available and cannot be directly approximated. We show how the bounds on the error between an interpolating polynomial and the true function can be used in the convergence theory of derivative free sampling methods. These bounds involve a constant that reflects the quality of the interpolation set. The main task of such a derivative free algorithm is to maintain an interpolation sampling set so that this constant remains small, and at least uniformly bounded. This constant is often described through the basis of Lagrange polynomials associated with the interpolation set. We provide an alternative, more intuitive, definition for this concept and show how this constant is related to the condition number of a certain matrix. This relation enables us to provide a range of algorithms whilst maintaining the interpolation set so that this condition number or the geometry constant remain uniformly bounded. We also derive bounds on the error between the model and the function and between their derivatives, directly in terms of this condition number and of this geometry constant. 相似文献
9.
In this paper, we combine the Galerkin–Lagrange multiplier (GLM) method with the two-level method to solve the stationary Navier–Stokes equations in order to avoid the time-consuming process and the construction of zero-divergence elements. Different quadrilateral partitions are used for approximating the velocity and the pressure. Then some error estimates are obtained and some numerical results of the GLM method and the two-level GLM method are given. The results show that the two-level method based on the GLM method is more efficient than the GLM method under the convergence rate of same order. 相似文献
10.
Emanuele Galligani 《Annali dell'Universita di Ferrara》2002,48(1):99-117
Sunto L’applicazione di noti metodi che utilizzano funzioni di tipo blending per la costruzione di funzioni bivariate C1 per l’interpolazione di dati, richiede la conoscenza delle derivate parziali del primo ordine ai vertici di una triangolazione
sottostante. In questo lavoro consideriamo il metodo proposto da Nielson, che consiste nel calcolare stime delle derivate
parziali del primo ordine minimizzando un opportuno funzionale quadratico, caratterizzato da parametri di tensione non negativi.
Scopo del lavoro è l’analisi di alcune proprietà particolari di questo funzionale per la costruzione di algoritmi efficienti
e robusti per la determinazione delle stime suddette delle derivate quando si ha a che fare con insiemi di dati di grandi
dimensioni.
Abstract
The application of widely known blending methods for constructingC
1 bivariate functions interpolating scattered data requires the knowledge of the partial derivatives of first order at the
vertices of an underlying triangulation. In this paper we consider the method proposed by Nielson that consists in computing
estimates of the first order partial derivatives by minimizing an appropriate quadratic functional, characterized by nonnegative
tension parameters. The aim of the paper is to analyse some peculiar properties of this functional in order to construct robust
and efficient algorithms for determining the above estimates of the derivatives when we are concerned with extremely large
data sets.
相似文献
11.
Recently, the study of the behavior of the Hermite–Fejér interpolants in the complex plane was initiated by L. Brutman and I. Gopengauz (1999, Constr. Approx.15, 611–617). It was shown that, for a broad class of interpolatory matrices on [−1, 1], the sequence of polynomials induced by Hermite–Fejér interpolation to f(z)≡z diverges everywhere in the complex plane outside the interval of interpolation [−1, 1]. In this note we amplify this result and prove that the divergence phenomenon takes place without any restriction on the interpolatory matrices. 相似文献
12.
S. A. Mohiuddine John Michael Rassias Abdullah Alotaibi 《Mathematical Methods in the Applied Sciences》2017,40(8):3017-3025
In this paper, we are introducing pertinent Euler–Lagrange–Jensen type k‐quintic functional equations and investigate the ‘Ulam stability’ of these new k‐quintic functional mappings f:X→Y, where X is a real normed linear space and Y a real complete normed linear space. We also solve the Ulam stability problem for Euler–Lagrange–Jensen alternative k‐quintic mappings. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
13.
S. P. Sidorov 《Numerical Algorithms》2007,44(3):273-279
Let , –1<x
1<...<x
n
<1. Denote , t∈(–1,1). Given a function f∈W we try to recover f(ζ) at fixed point ζ∈(–1,1) by an algorithm A on the basis of the information f(x
1),...,f(x
n
). We find the intrinsic error of recovery .
This work is supported by RFBR (grant 07-01-00167-a and grant 06-01-00003). 相似文献
14.
R. D. Riess 《BIT Numerical Mathematics》1973,13(3):338-343
This paper presents a procedure for obtaining error estimates for Hermite interpolation at the Chebyshev nodes {cos ((2j+1)/2n)}
j
=0n–1
–1x1, for functionsf(x) of various orders of continuity. The procedure is applicable in many cases when the usual Lagrangian error bound is not, and is a better bound, in general, when both are applicable. 相似文献
15.
S.M. Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant
nodes in [−1,1], In 2000, M. Rever generalized S.M. Lozinskii’s result to |x|α(0≤α≤1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|α(1<α<2). 相似文献
16.
Bernstein–Nikolskii inequalities and Riesz interpolation formula are established for eigenfunctions of Laplace operators and polynomials on compact homogeneous manifolds. 相似文献
17.
18.
《Mathematische Nachrichten》2018,291(13):2008-2023
We study complex interpolation of Herz‐type Triebel–Lizorkin spaces by using the Calderón product method. Additionally we present complex interpolation between Herz‐type Triebel–Lizorkin spaces and Triebel–Lizorkin spaces . Moreover, we apply these results to obtain the complex interpolation of Triebel–Lizorkin spaces equipped with power weights and between (or ) spaces and Herz spaces. 相似文献
19.
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
20.
We find necessary density conditions for Marcinkiewicz–Zygmund inequalities and interpolation for spaces of spherical harmonics in with respect to the Lp norm. Moreover, we prove that there are no complete interpolation families for p≠2. 相似文献