Numerical Computation Complex Error Function
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Faddeeva Function
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here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How to accurately calculate the error function erf(x) with a computer? up vote 9 down vote http://epubs.siam.org/doi/abs/10.1137/0707012 favorite 2 I am looking for an accurate algorithm to calculate the error function I have tried using the following formula, (Handbook of Mathematical Functions, formula 7.1.26), but the results are not accurate enough for the application. statistics algorithms numerical-methods special-functions share|cite|improve this question edited Oct 12 at 15:31 J. M. 53k5118254 asked Jul 20 '10 at 20:20 badp 6741225 You may want to take a look at python's code.google.com/p/mpmath or other libraries that advertise a "multiple precision" feature. Also, http://math.stackexchange.com/questions/97/how-to-accurately-calculate-the-error-function-erfx-with-a-computer this may be a better question for stack overflow instead, since it's more of a computer science thing. –Jon Bringhurst Jul 20 '10 at 20:26 @Jon: Nope, I'm not interested in a library, there is no such library for the language I'm writing in (yet). I need the mathematical algorithm. –badp Jul 20 '10 at 20:49 Have you tried numerical integration? Gaussian Quadrature is an accurate technique –Digital Gal Aug 28 '10 at 1:25 GQ is nice, but with (a number of) efficient methods for computing $\mathrm{erf}$ already known, I don't see the point. –J. M. Aug 29 '10 at 23:07 add a comment| 4 Answers 4 active oldest votes up vote 9 down vote accepted I am assuming that you need the error function only for real values. For complex arguments there are other approaches, more complicated than what I will be suggesting. If you're going the Taylor series route, the best series to use is formula 7.1.6 in Abramowitz and Stegun. It is not as prone to subtractive cancellation as the series derived from integrating the power series for $\exp(-x^2)$. This is good only for "small" arguments. For large arguments, you can use either the asymptotic series or the continued fraction representations. Otherwise, may I direct you to these papers by S. Winitzki that give nice approximations to the error function. (added on 5/4/2011) I wrote about the computation of the (complementary) error func
Mathematics Philadelphia, PA, USA tableofcontents doi>10.1137/0731077 1994 Article Bibliometrics http://dl.acm.org/citation.cfm?id=196013 ·Downloads (6 Weeks): n/a ·Downloads (12 Months): n/a ·Downloads (cumulative): n/a ·Citation Count: 12 Recent authors with related interests Concepts in this article powered by Concepts inComputations of the complex error function Error function In mathematics, the error function (also called the Gauss error function) error function is a special function of sigmoid shape which occurs in probability, statistics and partial differential equations. It is defined as: (When x is negative, the integral is interpreted as the negative of the integral from x to zero. morefromWikipedia Tools and Resources TOC Service: Email RSS Save numerical computation complex to Binder Export Formats: BibTeX EndNote ACMRef Share: | Author Tags algorithms complex error function computation of transforms fast fourier transform mathematical software measurement numerical analysis orthogonal rational expansions performance steepest descent theory Contact Us | Switch to single page view (no tabs) **Javascript is not enabled and is required for the "tabbed view" or switch to the single page view** Powered by The ACM Digital Library is published by the Association for Computing Machinery. Copyright © 2016 ACM, Inc. Terms of Usage Privacy Policy Code of Ethics Contact Us Useful downloads: Adobe Reader QuickTime Windows Media Player Real Player Did you know the ACM DL App is now available? Did you know your Organization can subscribe to the ACM Digital Library? The ACM Guide to Computing Literature All Tags Export Formats Save to Binder
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