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Numerical Analysis

Posted on 2000-02-14
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Last Modified: 2011-10-03
How can I calculate the 'Error Function'*  I need a full level of accuracy.  My current method of integrating using trapezium rule and simpson's rule etc.. are not accurate and too slow.  I need something like Excel must use uses to calculate to full accuracy in quick time.

Links to sites with algorithms or code would be ok, i'm envisaging some sort of convergent number sequence must exist.

*Integral of 2/sqrt(pi) * exp(-x**2)
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Question by:deighton
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6 Comments
 
LVL 14

Expert Comment

by:AlexVirochovsky
ID: 2520063
My advice : SAL
http://www.llp.fu-berlin.de/lsoft/B/1/index.shtml
It if source c/c++ codes for every
in Numeric Analysis!
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LVL 4

Accepted Solution

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jos010697 earned 200 total points
ID: 2522256
Bluntly stolen from Abramowitz and Stegun:

erf(x)= 1-e^(-x*x)*sum(i,1,5), a{i]*t^i) + e(x)

where t=1/(1+p*x)

where p= 0.3275911

where a[1]=  0.254829592
           a[2]= -0.284496736
           a[3]=  1.421413741
           a[4]=-1.453152027
           a[5]=1.061405429

The inaccuracy e(x) is at most 1.5E-7

kind regards,

Jos aka jos@and.nl
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LVL 18

Author Comment

by:deighton
ID: 2527970
That looks like an improvement on the formula I've got.

Code unusual not c?  I don't know how to code it into c.
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LVL 18

Author Comment

by:deighton
ID: 2528006
With some mods i'm getting good answers in VB

1 - Exp(-x ^ 2) * (0.254829592 * t - 0.284496736 * t ^ 2 + 1.421413741 * t ^ 3 - 1.453152027 * t ^ 4 + 1.061405429 * t ^ 5)

Is what I used.

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LVL 18

Author Comment

by:deighton
ID: 2528012
The e(x) at the end through me.
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LVL 4

Expert Comment

by:jos010697
ID: 2534086
The e(x) term is the absolute error (sic) of this approximation of the
error function; and, of course, it is not part of the approximation formula
itself ...

kind regards,

Jos aka jos@and.nl
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