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1.
Harten’s interpolatory multiresolution representation of data has been extended in the case of point-value discretization
to include Hermite interpolation by Warming and Beam in [17]. In this work we extend Harten’s framework for multiresolution analysis to the vector case for cell-averaged data, focusing
on Hermite interpolatory techniques.
*Supported by European Community IHP projects HPRN-CT-2002-00282 and HPRN-CT-2005-00286.
**Supported by European Community IHP projects HPRN-CT-2002-00282 and HPRN-CT-2005-00286, and by FPU grant from M.E.C.D. AP2000-1386.
†Supported by European Community IHP projects HPRN-CT-2002-00282 and HPRN-CT-2005-00286. 相似文献
2.
The interpolation of the market implied volatility function from several observations of option prices is often required in
financial practice and empirical study. However, the results from existing interpolation methods may not satisfy the property
that the European call option price function is monotonically decreasing and convex with respect to the strike price. In this
paper, a modified convex interpolation method (with and without smoothing) is developed to approximate the option price function
while explicitly incorporating the shape restrictions. The method is optimal for minimizing the distance between the implied
risk-neutral density function and a prior density function, which allows us to benefit from nonparametric methodology and
empirical experience. Numerical performance shows that the method is accurate and robust. Whether or not the sample satisfies
the convexity and decreasing constraints, the method always works.
H. Yin’s research was supported by FRG of Minnesota State University Mankato and Chinese NSF Grants 10671203, 70531040, and
70621001.
L. Qi’s work was supported by the Hong Kong Research Grant Council. 相似文献
3.
Ralf Siewer 《BIT Numerical Mathematics》2006,46(1):127-140
This paper is concerned with the construction of the fundamental functions associated with a two-point Hermite spline interpolation scheme used by Martensen in the context
of the remainder of the Gregory quadrature rule. We derive both a recursive construction and an explicit representation in terms of the underlying B-Splines which can easily be deduced using Marsden’s identity. We can make use of these functions
in order to introduce a local interpolation scheme which reproduces all splines. Finally, we examine the error of this interpolant
to a sufficiently smooth function and realize that it behaves like
in the case of splines of degree n.
AMS subject classification (2000) 65D05, 65D07, 41A15 相似文献
4.
Halley's method is a higher order iteration method for the solution of nonlinear systems of equations. Unlike Newton's method, which converges quadratically in the vicinity of the solution, Halley's method can exhibit a cubic order of convergence. The equations of Halley's method for multiple dimensions are derived using Padé approximants and inverse one-point interpolation, as proposed by Cuyt. The investigation of the performance of Halley's method concentrates on eight-node volume elements for nonlinear deformations using Staint Venant-Kirchhoff's constitutive law, as well as a geometric linear theory of von Mises plasticity. The comparison with Newton's method reveals the sensibility of Halley's method, in view of the radius of attraction but also demonstrates the advantages of Halley's method considering simulation costs and the order of convergence. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
V. M. Murzina 《Algebra and Logic》2007,46(6):409-418
We study into the question whether calculi associated with Ershov topological spaces possess Craig’s interpolation property.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
__________
Translated from Algebra i Logika, Vol. 46, No. 6, pp. 745–762, November–December, 2007. 相似文献
6.
L. L. Maksimova 《Algebra and Logic》2007,46(5):341-353
The interpolation property in extensions of Johansson’s minimal logic is investigated. The construction of a matched product
of models is proposed, which allows us to prove the interpolation property in a number of known extensions of the minimal
logic. It is shown that, unlike superintuitionistic, positive, and negative logics, a sum of J-logics with the interpolation property CIP may fail to possess CIP, nor even the restricted interpolation property.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
__________
Translated from Algebra i Logika, Vol. 46, No. 5, pp. 627–648, September–October, 2007. 相似文献
7.
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
8.
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
9.
Shaochun Chen 《Applied mathematics and computation》2011,217(22):9313-9321
In this paper, using the Newton’s formula of Lagrange interpolation, we present a new proof of the anisotropic error bounds for Lagrange interpolation of any order on the triangle, rectangle, tetrahedron and cube in a unified way. 相似文献
10.
Abstract. In this paper, we prove that Newton's method for convex best interpolation is locally quadratically convergent, giving an answer to a question of Irvine, Marin, and Smith [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. A damped Newton-type method is presented which has global quadratic convergence. Analogous results are obtained for the convex smoothing problem. Numerical examples are presented. 相似文献
11.
12.
Jinming Wu 《Mathematical Methods in the Applied Sciences》2014,37(11):1593-1601
In this article, we discuss a class of multiquadric quasi‐interpolation operator that is primarily on the basis of Wu–Schaback's quasi‐interpolation operator and radial basis function interpolation. The proposed operator possesses the advantages of linear polynomial reproducing property, interpolation property, and high accuracy. It can be applied to construct flexible function approximation and scattered data fitting from numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
13.
14.
Len Bos 《Journal of Computational and Applied Mathematics》2011,236(4):504-510
It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results suggest that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes. 相似文献
15.
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
16.
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
17.
18.
A. Bathi Kasturiarachi 《International Journal of Mathematical Education in Science & Technology》2013,44(4):521-527
Using Newton's method as an intermediate step, we introduce an iterative method that approximates numerically the solution of f (x) = 0. The method is essentially a leap-frog Newton's method. The order of convergence of the proposed method at a simple root is cubic and the computational efficiency in general is less, but close to that of Newton's method. Like Newton's method, the new method requires only function and first derivative evaluations. The method can easily be implemented on computer algebra systems where high machine precision is available. 相似文献
19.
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
20.
Lagrange插值和Hermite-Fejér插值在Wiener空间下的平均误差 总被引:1,自引:0,他引:1
在L_q-范数逼近的意义下,确定了基于Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列在Wiener空间下的p-平均误差的弱渐近阶.从我们的结果可以看出,当2≤q<∞,1≤p<∞时,基于第一类Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列的p-平均误差弱等价于相应的最佳逼近多项式列的p-平均误差.在信息基计算复杂性的意义下,如果可允许信息泛函为计算函数在固定点的值,那么当1≤p,q<∞时,基于第一类Chebyshev多项式零点的Lagrange插值多项式列和Hermite-Fejér插值多项式列在Wiener空间下的p-平均误差弱等价于相应的最小非自适应p-平均信息半径. 相似文献