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On a Numerical Differentiation
SIAM Journal on Numerical Analysis, 1986Betrachtet 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
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Numerical differentiation by integration
Mathematics of Computation, 2013While 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 +2 more
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Numerical Differentiation and Regularization
SIAM Journal on Numerical Analysis, 1971Tikhonov’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
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Formulae for Numerical Differentiation
The Mathematical Gazette, 1941In a recent paper (1) formulae were given for the numerical integration of a function in terms of its values at a set of arguments at equal intervals. In this companion paper, formulae for numerical differentiation, using the same data, are collected. Their utility in enabling derivatives of a function given numerically at such a set of arguments to be
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BIT, 1975
In a recent paper Strom analyzed a simple extrapolation algorithm for numerical differentiation and derived certain properties about the kernel function of the integral representation of the remainder term. These properties are useful for placing bounds on the error in cases when specified higher order derivatives are known not to change sign.
Ström, Torsten, Lyness, J. N.
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In a recent paper Strom analyzed a simple extrapolation algorithm for numerical differentiation and derived certain properties about the kernel function of the integral representation of the remainder term. These properties are useful for placing bounds on the error in cases when specified higher order derivatives are known not to change sign.
Ström, Torsten, Lyness, J. N.
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Numerical Differentiation of Analytic Functions
ACM Transactions on Mathematical Software, 1981It 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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