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| Question about gqgenerategaussjacobi http://forum.alglib.net/viewtopic.php?f=2&t=33 |
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| Author: | MKl [ Wed Jun 23, 2010 2:56 pm ] |
| Post subject: | Question about gqgenerategaussjacobi |
Hello, I'm using the routine gqgenerategaussjacobi to generate points and weights for Gauss-Jacobi integration. When debugging my code I observed that the weights of the generated rules don't add up to 1, but rather to 1.0666... . Is this intentionally? And if the answer is yes, is there any particular reason for choosing the weights in such way? Thanks for your answers. |
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| Author: | Sergey.Bochkanov [ Wed Jun 23, 2010 4:56 pm ] |
| Post subject: | Re: Question about gqgenerategaussjacobi |
MKl wrote: I'm using the routine gqgenerategaussjacobi to generate points and weights for Gauss-Jacobi integration. When debugging my code I observed that the weights of the generated rules don't add up to 1, but rather to 1.0666... It's alright. Sum of weights is equal to integral(a,b,1*W(x)dx) (try to calculate this integral using Gauss-Jacobi formula and you will see why). This integral is equal to 2.0 only in the Gauss-Legendre case (alpha=beta=0.0). Note - to 2.0, not to 1.0. In the general case it may have arbitrary value. |
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| Author: | MKl [ Fri Jun 25, 2010 10:56 pm ] |
| Post subject: | Re: Question about gqgenerategaussjacobi |
Thank you for your reply. I'm using Gauss-Jacobi rules to calculate the expectation of functions of beta distributed variables and therefore expected the sum of weights to be one. Thanks again for pointing out my mistake. |
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