Results 191 to 200 of about 1,666,189 (240)

On error backpropagation algorithm using absolute error function

IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028), 2003
We propose error backpropagation using the absolute error function as an objective function. The error backpropagation is the most popular learning algorithm for multi-layered neural networks. In the error backpropagation, the square error function is usually used as the objective function. But a square function has a drawback in which it is enormously
K. Taji, T. Miyake, H. Tamura
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A Kuczma-type functional inequality for error and complementary error functions

Aequationes mathematicae, 2014
The error, resp. complementary error functions are defined by \[ \text{erf}(x)= {2\over\sqrt{\pi}} \int^x_0 e^{-t^2}\,dt, \] and \(\text{erf}_c(x)= 1-\text{erf}(x)\). Inspired by an interesting functional equation by \textit{M. Kuczma} [Rocz. Nauk.-Dydakt., Pr. Mat. 13, 197--213 (1993; Zbl 0964.39501)], namely \(x+ F(y+G(x))= y+F(x+ G(y))\), the author
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Functional inequalities for the error function

Aequationes mathematicae, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Computation of the Complex Error Function

SIAM Journal on Numerical Analysis, 1994
The paper gives an expansion of the error function (normal probability function) for complex values of the argument. The expansion is in terms of rational functions. Asymptotic properties of the coefficients of the expansion are studied and a compact Matlab program is given. A comparison is made with other algorithms from the literature.
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Approximation of the Complementary Error Function

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1995
The author gives a simple approximation to the complementary error function.
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Cubature Error Constants for Analytic Functions

SIAM Journal on Numerical Analysis, 1974
The purpose of this paper is to present a method for estimating the error constants required for the application of a cubature error bound due to Chawla [2].
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Specification Error Tests and Investment Functions

Econometrica, 1976
This paper analyzes three quarterly investment models for the detection of certain specifi- cation errors. The models are those of Anderson (1 and 2), Eisner (4), and Meyer-Glauber (10). The models are applied to thirteen manufacturing industries. A set of specification error tests developed by Ramsey (12, 13, and 14) are applied to the above models so
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Error and probability functions

2017
Like the gamma and psi functions, the functions treated in this chapter are among the most important of the special functions.
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Functional inequalities for the error function, II

Aequationes mathematicae, 2009
Let $${\rm erf}(x) = \frac{2} {\sqrt{\pi}} \int_0^x e^{-t^{2}} dt$$ be the error function. We prove that the following inequalities are valid for all positive real numbers x, y with \(x \leq y\): $${\rm erf}(1) < \frac {{\rm erf} (x + {\rm erf}(y))} {{\rm erf}(y + {\rm erf}(x))} < \frac{2} {\sqrt{\pi}} \quad {\rm and} \quad 0 < \frac{{\rm ...
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Error Function Subroutine

American Journal of Physics, 1974
Donald L. Shirer, Robert M. Hashway
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