Results 241 to 250 of about 95,553 (284)

Heuristic regularization methods for numerical differentiation [PDF]

Computers and Mathematics With Applications, 2012
In this paper, we use smoothing splines to deal with numerical differentiation. Some heuristic methods for choosing regularization parameters are proposed, including the L-curve method and the de Boor method.
D Lesnic
exaly   +2 more sources

Discrete mollification and automatic numerical differentiation [PDF]

Computers and Mathematics With Applications, 1998
An automatic method for numerical differentiation, based on discrete mollification and the principle of generalized cross validation is presented. With data measured at a discrete set of points of a given interval, the method allows for the approximate ...
D A Murio
exaly   +2 more sources

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On a Numerical Differentiation

SIAM Journal on Numerical Analysis, 1986
Betrachtet werden numerische Differentiationsformeln des Typs \[ f^{(m)}(x)\approx (1/h^ m)\sum^{n}_{i=1}a_ if(x+hb_ i),\quad b_ i\neq b_ j\text{ für }i\neq j \] vom Grad \(n-m\). Der Grad kann zwar auch \(n-m+1\) sein, aber niemals \(\geq n-m+2\). Dafür, daß der Grad der Formel \(n-m+1\) ist, wird eine notwendige und hinreichende Bedingung angegeben ...
Herceg, Dragoslav, Cvetković, Ljiljana
openaire   +2 more sources

Numerical differentiation by integration

Mathematics of Computation, 2013
While there are various methods which have been developed for numerical differentiation, the estimation of the derivative of a function is often problematic when one has only noisy values of the function itself. In this instance it is important to employ a method which is able to calculate \(f'(x)\) in a stable manner. This article specifically focuses
Xiaowei Huang 0003, Chuansheng Wu, Jun Zhou   +2 more
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Numerical differentiation for two-dimensional scattered data [PDF]

Journal of Mathematical Analysis and Applications, 2005
In this paper, we propose a regularization method for numerical differentiation of two-dimensional mildly scattered input data. A regularized solution is constructed based on the Green's function.
Ting Wei
exaly   +2 more sources

Numerical differentiation for high orders by an integration method [PDF]

Journal of Computational and Applied Mathematics, 2010
This paper mainly studies the numerical differentiation by integration method proposed first by Lanczos. New schemes of the Lanczos derivatives are put forward for reconstructing numerical derivatives for high orders from noise data. The convergence rate
Zewen Wang
exaly   +2 more sources

Numerical Differentiation and Regularization

SIAM Journal on Numerical Analysis, 1971
Tikhonov’s regularization procedure is applied to the operation of differentiation, resulting in a procedure for numerical differentiation for which the effects of errors in the values of the function being differentiated on the values for the derivative obtained in the procedure can be studied. The theoretical discussion is complemented by the results
openaire   +2 more sources

A new approach to numerical differentiation [PDF]

Journal of Computational and Applied Mathematics, 2009
In this paper we consider the numerical differentiation of functions specified by noisy data. A new approach, which is based on an integral equation of the first kind with a suitable compact operator, is presented and discussed. Since the singular system
Zhenyu Zhao, Zehong Meng, Guoqiang He
exaly   +2 more sources

Numerical Differentiation of Analytic Functions

ACM Transactions on Mathematical Software, 1981
It is well known that the classical difference formulas for evaluating high derivatives of a real function f(ζ) are very ill-conditioned. However, if the function f(ζ) is analytic and can be evaluated for complex values of ζ, the problem can be shown to be perfectly well-conditioned.
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Error formulas for divided difference expansions and numerical differentiation [PDF]

Journal of Approximation Theory, 2003
We derive an expression for the remainder in divided difference expansions and use it to give new error bounds for numerical ...
Michael S Floater
exaly   +2 more sources