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991.
Loredana Coluccio Alfredo EisinbergGiuseppe Fedele 《Journal of Computational and Applied Mathematics》2008
The aim of this paper is to transform a polynomial expressed as a weighted sum of discrete orthogonal polynomials on Gauss–Lobatto nodes into Bernstein form and vice versa. Explicit formulas and recursion expressions are derived. Moreover, an efficient algorithm for the transformation from Gauss–Lobatto to Bernstein is proposed. Finally, in order to show the robustness of the proposed algorithm, experimental results are reported. 相似文献
992.
The best rate of approximation of functions on the sphere by spherical polynomials is majorized by recently introduced moduli
of smoothness. The treatment applies to a wide class of Banach spaces of functions.
相似文献
993.
Chelo Ferreira Jos L. Lpez Ester Prez Sinusía 《Journal of Computational and Applied Mathematics》2008,217(1):88-109
It has been shown in Ferreira et al. [Asymptotic relations in the Askey scheme for hypergeometric orthogonal polynomials, Adv. in Appl. Math. 31(1) (2003) 61–85], López and Temme [Approximations of orthogonal polynomials in terms of Hermite polynomials, Methods Appl. Anal. 6 (1999) 131–146; The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis, J. Comput. Appl. Math. 133 (2001) 623–633] that the three lower levels of the Askey table of hypergeometric orthogonal polynomials are connected by means of asymptotic relations. In Ferreira et al. [Limit relations between the Hahn polynomials and the Hermite, Laguerre and Charlier polynomials, submitted for publication] we have established new asymptotic connections between the fourth level and the two lower levels. In this paper, we continue with that program and obtain asymptotic expansions between the fourth level and the third level: we derive 16 asymptotic expansions of the Hahn, dual Hahn, continuous Hahn and continuous dual Hahn polynomials in terms of Meixner–Pollaczek, Jacobi, Meixner and Krawtchouk polynomials. From these expansions, we also derive three new limits between those polynomials. Some numerical experiments show the accuracy of the approximations and, in particular, the accuracy in the approximation of the zeros of those polynomials. 相似文献
994.
Bruce Curry 《Computational Management Science》2007,4(3):227-242
This paper deals with feedforward neural networks containing a single hidden layer and with sigmoid/logistic activation function.
Training such a network is equivalent to implementing nonlinear regression using a flexible functional form, but the functional
form in question is not easy to deal with. The Chebyshev polynomials are suggested as a way forward, providing an approximation
to the network which is superior to Taylor series expansions. Application of these approximations suggests that the network
is liable to a ‘naturally occurring’ parameter redundancy, which has implications for the training process as well as certain
statistical implications. On the other hand, parameter redundancy does not appear to damage the fundamental property of universal
approximation.
相似文献
995.
McCoy环的扩张(英文) 总被引:1,自引:1,他引:0
A ring R is said to be right McCoy if the equation f(x)g(x)=0,where f(x)and g(x)are nonzero polynomials of R[x],implies that there exists nonzero s∈R such that f(x)s=0.It is proven that no proper(triangular)matrix ring is one-sided McCoy.It is shown that for many polynomial extensions,a ring R is right McCoy if and only if the polynomial extension over R is right McCoy. 相似文献
996.
Marie-Laurence Mazure 《Advances in Computational Mathematics》2004,20(1-3):177-203
It is now classical to define blossoms by means of intersections of osculating flats. We consider here the most general context of spline spaces with sections in arbitrary extended Chebyshev spaces and with connections defined by arbitrary lower triangular matrices with positive diagonal elements. We show how the existence of blossoms in such spaces automatically leads to optimal bases in the sense of Carnicer and Peña. 相似文献
997.
Teresa Martinez 《Mathematische Nachrichten》2008,281(7):978-988
We define and investigate the multipliers of Laplace transform type associated to the differential operator Lλf (θ) = –f ″(θ) – 2λ cot θf ′(θ) + λ2f (θ), λ > 0. We prove that these operators are bounded in Lp ((0, π), dmλ) and of weak type (1, 1) with respect to the same measure space, dmλ (θ) = (sin θ)2λ dθ. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
998.
We prove that the classical model of an infectious disseise, which never kills and which does not induce autoimmunity, is integrable. This model can be written as x′=−bxy−mx+cy+mk, y′=bxy−(m+c)y with parameters b,c,k,m∈R. We provide the explicit expression of its first integrals and of the set of all its invariant algebraic curves. 相似文献
999.
Francisco Perez Acosta 《计算数学(英文版)》1998,(6)
1.IntroductionLetfbeacontinuousfunctionon[a,b].L[.willdesignatethesetofallpolynomialsofdegreelessorequalthannand11thesetofallpolyflomials.Asiswellknown,foreachntheminimaxoffisgivenby:wherepnisthebestuniformapproximationoffin11..LetusalsoconsidertileminimaxseriesgivenbytheexpressionThesetoffunctionsforwhichS*(f)=ZEd(f)相似文献
1000.
Tran Ngoc Lien 《Journal of Mathematical Analysis and Applications》2008,337(2):1302-1314
We consider the problem of finding a function defined on (0,∞) from a countable set of values of its Laplace transform. The problem is severely ill-posed. We shall use the expansion of the function in a series of Laguerre polynomials to convert the problem in an analytic interpolation problem. Then, using the coefficients of Lagrange polynomials we shall construct a stable approximation solution. Error estimate is given. Numerical results are produced. 相似文献