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Computing in Science & Engineering, 2021
Prompted by previous work published in this magazine, in this article we focus on the derivation of global analytical bounds for the error function of a real argument. Using an integral representation of this function, we obtain two simple and accurate lower bounds, which complement a well-known upper bound given long ago by Polya.
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Prompted by previous work published in this magazine, in this article we focus on the derivation of global analytical bounds for the error function of a real argument. Using an integral representation of this function, we obtain two simple and accurate lower bounds, which complement a well-known upper bound given long ago by Polya.
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Computing in Science & Engineering, 2010
A new exact representation of the error function of real arguments justifies an accurate and simple analytical approximation. Two of the most widely used functions in physical sciences are the error function erf(x) and its related complimentary error function erfc(x). These functions occur extensively in problems relating to diffusion, heat conduction,
Mohankumar Nandagopal +2 more
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A new exact representation of the error function of real arguments justifies an accurate and simple analytical approximation. Two of the most widely used functions in physical sciences are the error function erf(x) and its related complimentary error function erfc(x). These functions occur extensively in problems relating to diffusion, heat conduction,
Mohankumar Nandagopal +2 more
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Error-Robust Functional Dependencies
Fundamenta Informaticae, 2004A database user may be confronted with a relation that contains errors. These errors may result from transmission through a noisy channel, or they may have been added deliberately in order to hide or spoil information. Error-robust functional dependencies provide dependencies that still hold in the case of errors.
Sven Hartmann +3 more
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Advances in Computational Mathematics, 2009
The Gauss error function of a real variable is defined by \(\text{erf}(x)= {2\over\sqrt{\pi}} \int^x_0 e^{-t^2}\,dt\). Results on the error function may be found e.g., in the well-known monographs by Abramowitz-Stegun (1965), Gradshteyn-Ryzhik (1994), or Luke (1975).
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The Gauss error function of a real variable is defined by \(\text{erf}(x)= {2\over\sqrt{\pi}} \int^x_0 e^{-t^2}\,dt\). Results on the error function may be found e.g., in the well-known monographs by Abramowitz-Stegun (1965), Gradshteyn-Ryzhik (1994), or Luke (1975).
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Statistics & Risk Modeling, 1983
The paper deals with the problem whether approximations to distributions of estimators (e.g., normal approximations or Edgeworth expansions) can be used for obtaining approximations of risks. It is shown that for loss functions with ''diminishing increment'', the relative errors of the approximating risk functions can be computed from the errors of the
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The paper deals with the problem whether approximations to distributions of estimators (e.g., normal approximations or Edgeworth expansions) can be used for obtaining approximations of risks. It is shown that for loss functions with ''diminishing increment'', the relative errors of the approximating risk functions can be computed from the errors of the
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SeMA Journal, 2014
After exploring the particular situation of a non-variational elliptic equation, we introduce the formal concept of an error functional as a generalization of the intuitive idea of a non-negative functional whose only possible critical value is zero. The main result we prove is that such an error is a true measure of how far we are from the zero set of
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After exploring the particular situation of a non-variational elliptic equation, we introduce the formal concept of an error functional as a generalization of the intuitive idea of a non-negative functional whose only possible critical value is zero. The main result we prove is that such an error is a true measure of how far we are from the zero set of
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Ray tomography: Errors and error functions
Journal of Applied Geophysics, 1994Tomography is the inversion of boundary projections to reconstruct the internal characteristics of the medium between the source and detector boreholes. Tomography is used to image the structure of geological formations and localized inhomogenieties. This imaging technique may be applied to either seismic or electromagnetic data, typically recorded as ...
J.C. Santamarina, A.C. Reed
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1995
Abstract In previous chapters we have made use of the sum-of-squares error function, which was motivated primarily by analytical simplicity. There are many other possible choices of error function which can also be considered, depending on the particular application.
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Abstract In previous chapters we have made use of the sum-of-squares error function, which was motivated primarily by analytical simplicity. There are many other possible choices of error function which can also be considered, depending on the particular application.
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The zeros of the complementary error function
Numerical Algorithms, 2008We show that the complementary error function, $\text{erfc} (z)= \frac{2}{\sqrt{\pi}}\int_z^{\infty}{e^{-s^2} \text{d}s}$ , has no zeros in $\text{D}= \left\{ z : \frac{3}{4} \ \pi \le Arg z
LAFORGIA, Andrea Ivo Antonio, A. ELBERT
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