共查询到20条相似文献,搜索用时 250 毫秒
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<正> 函数图像对阐述和研究函数的性质起着重要作用。本文所要介绍的是利用导函数的图像来帮助研究函数。由于导函数的图像可使函数、导数、二阶导数的几何解释能同时出现在一个图形里,因而对探导函数、导数、二阶导数三者之间组合成的关系起着直观启发作用,利 相似文献
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We present a new third order method for finding multiple roots of nonlinear equations based on the scheme for simple roots developed by Kou et al. [J. Kou, Y. Li, X. Wang, A family of fourth-order methods for solving non-linear equations, Appl. Math. Comput. 188 (2007) 1031-1036]. Further investigation gives rise to new third and fourth order families of methods which do not require second derivative. The fourth order family has optimal order, since it requires three evaluations per step, namely one evaluation of function and two evaluations of first derivative. The efficacy is tested on a number of relevant numerical problems. Computational results ascertain that the present methods are competitive with other similar robust methods. 相似文献
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Sanjay Kumar Khattri 《Mathematics in Computer Science》2011,5(2):237-243
We develop an eighth order family of methods, consisting of three steps and three parameters, for solving nonlinear equations.
Per iteration the methods require four evaluations (three function evaluations and one evaluation of the first derivative).
Convergence analysis shows that the family is eighth-order convergent which is also substantiated through the numerical work.
Computational results ascertain that family of methods are efficient and demonstrate equal or better performance as compared
with other well known methods. 相似文献
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We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order β∈(0, 2] and the first-order time derivative with Caputo derivative of order α∈(0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation. 相似文献
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Paul Glasserman 《Annals of Operations Research》1992,39(1):41-67
This paper establishes connections between two derivative estimation techniques:infinitesimal perturbation analysis (IPA) and thelikelihood ratio orscore function method. We introduce a systematic way of expanding the domain of the former to include that of the latter, and show that many likelihood ratio derivative estimators are IPA estimators obtained in a consistent manner through a special construction. Our extension of IPA is based onmultiplicative smoothing. A function with discontinuities is multiplied by asmoothing complement, a continuous function that takes the value zero at a jump of the first function. The product of these functions is continuous and provides an indirect derivative estimator after an appropriate normalization. We show that, in substantial generality, the derivative of a smoothing complement is a randomized score function: its conditional expectation is a derivative of a likelihood ratio. If no conditional expectation is applied, derivative estimates based on multiplicative smoothing have higher variance than corresponding estimates based on likelihood ratios. 相似文献
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A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order α ∈ (0, 1], and the second-order space derivative is replaced with a Riesz-Feller derivative of order β ∈ (0, 2]. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives. 相似文献
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Liang Meili 《Journal of Mathematical Analysis and Applications》2009,356(1):201-207
In this paper, we investigate the value distribution of an algebroid function and its derivative, and obtain two inequations between Nevanlinna characteristic function of an algebroid function and that of its derivative. We extend Chuang Chitai's theorem of meromorphic functions to algebroid functions. 相似文献
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We consider the problem of finding necessary and sufficient conditions for validity of an estimate for a function by some differential operation containing a weight function rather than the ordinary derivative. This operation is referred to as the -weighted derivative. 相似文献
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B. D. Gel'man 《Functional Analysis and Its Applications》2001,35(3):183-188
We prove a theorem generalizing the classical implicit function theorem to the case in which the derivative of the map is a surjective continuous linear operator. We do not assume that the kernel of the derivative is a complemented subspace. 相似文献
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M. C. Jones 《Annals of the Institute of Statistical Mathematics》1992,44(4):721-727
To estimate the quantile density function (the derivative of the quantile function) by kernel means, there are two alternative approaches. One is the derivative of the kernel quantile estimator, the other is essentially the reciprocal of the kernel density estimator. We give ways in which the former method has certain advantages over the latter. Various closely related smoothing issues are also discussed. 相似文献
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《Comptes Rendus Mathematique》2014,352(7-8):651-654
We consider the functional generalized linear model whose response function is a linear operator depending on an explanatory variable X belonging to a functional space. It has been studied, among others, by Cardot and Sarda [4]. In this paper, we consider the functional generalized linear model with derivative component, denoted MLGFD in the following, whose response function depends on a linear operator of X and on its derivative. We propose estimators for the unknown functional parameters and provide convergence rates. 相似文献