Accuracy of Integral with epsilon
10-09-2021, 09:50 PM
Post: #19
 robve Member Posts: 287 Joined: Sep 2020
RE: Accuracy of Integral with epsilon
(10-09-2021 02:22 AM)Valentin Albillo Wrote:  Someone here is not paying attention.

Are you saying that a complex state-of-the-art Tanh-Sinh method requires 27 evaluations of the integrand (the constant 2) to integrate the constant 2 from -10 to 10 ? Really !?

What a lousy implementation !

You do realize that it is a fallacy to assume exp(x) and cosh(x)+sinh(x) equate numerically, in addition to algebraically?

For one, sinh(x) typically uses expm1(x)=exp(x)-1 for higher accuracy sinh(x) = (z+z/(z+1))/2 with z=expm1(x). This asymmetrically affects cosh(x)+sinh(x) for x<0. The difference grows with smaller x<0, which is easy to see when we plug in expm1(x).

- Rob

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 Messages In This Thread Accuracy of Integral with epsilon - lrdheat - 10-08-2021, 09:57 PM RE: Accuracy of Integral with epsilon - toml_12953 - 10-08-2021, 10:17 PM RE: Accuracy of Integral with epsilon - Thomas Okken - 10-08-2021, 10:18 PM RE: Accuracy of Integral with epsilon - toml_12953 - 10-08-2021, 10:28 PM RE: Accuracy of Integral with epsilon - lrdheat - 10-08-2021, 11:28 PM RE: Accuracy of Integral with epsilon - toml_12953 - 10-09-2021, 12:47 AM RE: Accuracy of Integral with epsilon - robve - 10-09-2021, 01:41 AM RE: Accuracy of Integral with epsilon - Valentin Albillo - 10-09-2021, 02:22 AM RE: Accuracy of Integral with epsilon - Paul Dale - 10-09-2021, 02:27 AM RE: Accuracy of Integral with epsilon - Thomas Okken - 10-09-2021, 08:47 AM RE: Accuracy of Integral with epsilon - John Keith - 10-09-2021, 05:40 PM RE: Accuracy of Integral with epsilon - robve - 10-09-2021, 08:37 PM RE: Accuracy of Integral with epsilon - Claudio L. - 10-12-2021, 04:47 PM RE: Accuracy of Integral with epsilon - robve - 10-14-2021, 02:43 AM RE: Accuracy of Integral with epsilon - robve - 10-09-2021 09:50 PM RE: Accuracy of Integral with epsilon - Albert Chan - 10-10-2021, 11:51 AM RE: Accuracy of Integral with epsilon - robve - 10-10-2021, 02:07 PM RE: Accuracy of Integral with epsilon - robve - 10-09-2021, 02:01 PM RE: Accuracy of Integral with epsilon - lrdheat - 10-09-2021, 03:13 AM RE: Accuracy of Integral with epsilon - toml_12953 - 10-09-2021, 05:44 AM RE: Accuracy of Integral with epsilon - toml_12953 - 10-09-2021, 11:26 AM RE: Accuracy of Integral with epsilon - lrdheat - 10-09-2021, 05:16 AM RE: Accuracy of Integral with epsilon - lrdheat - 10-09-2021, 03:25 PM

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