Linked Questions
12 questions linked to/from Numerical underflow for a scaled error function
0
votes
1
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330
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Trying to compute erfcx(x)? [duplicate]
The function erfcx(x) = exp(x^2)erfc(x) is sometimes provided in numerical packages to avoid numerical underflow for large values of ...
- 11.1k
40
votes
2
answers
2k
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Is it possible to make Mathematica reformulate an expression in a more numerically stable way?
I'm writing a numerical optimization, and I'm having a problem with an expression of the form
$$ e^{-t} (1+\mathrm{erf}(t)) $$
The overall shape of the function looks correct, but when $t$ is small, $...
- 473
14
votes
4
answers
1k
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Implementing a compilable Faddeeva function of complex argument
For those, who are looking at Halirutan's answer and thinking "gee, I wish I was that good at LibraryLink, then I could really speed up my code!" I leave here the ...
- 11.4k
15
votes
4
answers
661
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Terrible accuracy of DawsonF
DawsonF[30.] returns 0. The correct value is 0.016676...
At least it prints a warning message,
...
- 11.1k
3
votes
3
answers
716
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How can I compute Erf of large numbers to more precision?
I would like to compute Erf[80/3] to enough precision to know the order of magnitude of 1 - Erf[80/3]
How can I do that?
I ...
- 457
9
votes
2
answers
846
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Analytical approximation of indefinite integral on a given interval to a given precision
I'm looking for an analytical approximation of
$\int_a^b e^{-x^2}\mathrm{erf}(x+c) dx$
that would be accurate to precision $\varepsilon$ for $a,b,c$ within a certain range. How do I ask Mathematica ...
- 757
4
votes
2
answers
1k
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How to find the maximum of this function on the positive real line?
I need to maximize this function on the positive real line:
$$
\frac{1}{\Gamma(x)^{14}}\cdot\frac{1}{{\frac{323.6}{14x}}^{14x}}\cdot(1.22578*10^{19})^{x-1}e^{-14x}
$$
the correct answer should be ...
- 165
5
votes
2
answers
1k
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Assigning an analytical approximation to the error function erf(x)
Working with some iterative integral equations, I have Gaussian density functions involved therein. Integrating the Gaussian function I obtain the error function. When I take the second integration, ...
- 2,435
1
vote
1
answer
1k
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Error Function Integral (Erf)
Any idea how to solve analytically this integral
Integrate[(a Erf[a Sqrt[b/(a^2 + b)] c])/(a^2 + b)^(3/2), a]
I tried substitution u=a^2 + b, but it didn't work. ...
- 347
1
vote
1
answer
337
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Calculate an integration limit to obtain a certain area under a curve
I have a function that looks like a sigmoid curve. I would like to calculate the right integration limit so that the area under the sigmoid curve has a given value.
my curve:
...
- 910
-1
votes
2
answers
181
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Roots of expressions involving the complementary error function
I have an expression as follows
...
- 1,248
0
votes
2
answers
76
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Same integral yielding to different results
I am currently working with the following integrals
\begin{equation}
\int_{0}^{\infty} dk\thinspace \frac{k^{3}e^{-2kd}}{\omega^{2}+k^{4}} = \frac{1}{\omega^{2}d^{4}}\int_{0}^{\infty}d\epsilon\...
- 573