Difference in MATLAB function evaluation
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According to the properties of gamma function, for any x > 0
But when I try to use it in MATLAB, it shows a very large error
gamma(150) - 149*gamma(149)
ans =
-1.5240e+247
Can anybody explain the reason for this? I need it for an approximation algorithm I am trying to develop.
Thanks in advance.
1 个评论
Star Strider
2017-1-31
FWIW, I get similar results for these (in R2016b):
n = 149;
q1 = gamma(n+1) - n*gamma(n);
q2 = gamma(n+1) - factorial(n);
q3 = gamma(n+1) - prod(1:n);
q1 =
-15.2402e+246
q2 =
-819.3656e+243
q3 =
-819.3656e+243
I hope this is a problem with my understanding of the gamma function, and not a problem with its implementation in MATLAB.
采纳的回答
Honglei Chen
2017-1-31
For your use case, 150! is a very large number so the numerical precision issue starts to kick in. I'd suggest you to use gammaln instead, for example, you can do
gammaln(150)-(log(149)+gammaln(149))
and the result is indeed 0.
HTH.
更多回答（1 个）
While the absolute error is huge, the relative error is tiny:
(gamma(150) - 149*gamma(149)) / gamma(150)
>> -3.9868e-014
This is the expected error caused by using the IEEE754 double format. This stores about 16 valid digits.
If an approxmation algorithm is sensitive for this difference, it is instable and of limited use.
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