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GeezerVison is showing mathworld.wolfram.com — Error Function -- from Wolfram MathWorld

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Error Function


The term error function has two common mathematical uses. In the theory of special functions, it denotes erf, the entire function defined for a complex number z by

 erf(z)=2/(sqrt(pi))int_0^ze^(-t^2)dt.

This function occurs in integrals involving the normal distribution.

In optimization theory, an error function can instead mean an objective function to be minimized. In this usage, it is often also called a loss function (Goodfellow et al. 2016, p. 80).


See also

Erf, Loss Function, Objective Function

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References

Goodfellow, I.; Bengio, Y.; and Courville, A. Deep Learning. Cambridge, MA: MIT Press, p. 80, 2016. https://www.deeplearningbook.org/contents/numerical.html.National Institute of Standards and Technology. "Error Functions" and "Statistics." §§7.2(i) and 7.20(iii) in NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/7.2.i. https://dlmf.nist.gov/7.20.iii.

Referenced on Wolfram|Alpha

Error Function

Cite this as:

Weisstein, Eric W. "Error Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ErrorFunction.html

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