The literature on meshless methods observed that kernel-based numerical differentiation formulae are robust and provide high accuracy at low cost. This paper analyzes the error of such formulas, using the new technique of growth functions. It allows to bypass certain technical assumptions that were needed to prove the standard error bounds on interpolants and their derivatives. Since differenti...

Previously, based on the method of (radial powers) radial basis functions, we proposed a procedure for approximating derivative values from one-dimensional scattered noisy data. In this work, we show that the same approach also allows us to approximate the values of (Caputo) fractional derivatives (for orders between 0 and 1). With either an a priori or a posteriori strategy of choosing the reg...

A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are presented. These examples show that the proposed method for stable numerical differentiation is n...

In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...

abstract. in recent years several studies have shown that  control charts with adaptive schemes or double sampling plans detect both small and moderate shifts in the process mean more quickly than the traditional shewhart  chart. in the classical double sampling  chart, the difference between two points were placed in the central region of first stage was not considered. in this study, a new co...

In this article, we present investigations on several techniques for numerical differentiation of data. Local techniques are confronted with global approaches and the differences are discussed in detail. Two basic quantities are used for characterization of results: The variance of the difference of the true derivative and its estimate, and the smoothness of the estimate. We apply the different...

In many scientific applications, it is necessary to compute the derivative of functions specified by data. Conventional finite-difference approximations will greatly amplify any noise present in the data. Denoising the data before or after differentiating does not generally give satisfactory results see an example in Section 4 . A method which does give good results is to regularize the differe...

Practical methods of differentiating a signal known only through its on-line samples are much needed, given the numerous areas in control theory and practice where differentiation is encountered. This communication presents theoretical as well as implementation details on several numerical differentiation algorithms which may be useful in the area of nonlinear estimation. In particular, these a...

Article history: Received 7 July 2008 Received in revised form 15 January 2009 Accepted 10 February 2009 Available online xxxx PACS: 02.60.Jh 02.60.Pn 02.70.Bf

We describe several methods for the numerical approximation of a first derivative of a smooth real-valued univariate function for which only discrete noise-contaminated data values are given. The methods allow for both uniformly distributed and non-uniformly distributed abscissae. They are compared for accuracy on artificial data sets constructed by adding Gaussian noise to simple test function...