Re: References for Numerical Integration

[Dirk Laurie <dirk.laurie@gmail.com>]

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Have a look at Chapters 1 and 9 of the book "The SIAM 100-digit
Challenge: a Study in High-Accuracy Numerical Computing".
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Pari-GP 2.2.8 code (inter alia) is on the site:
http://www-m3.ma.tum.de/m3old/bornemann/challengebook

-- Dirk
Op So., 21 Okt. 2018 om 19:35 het kevin lucas <lucaskevin296@gmail.com> geskryf:
>
> PARI obviously has some very powerful tools for numerical integration. I have, however, keenly felt the absence of a text treating this area in more detail than the manual. I was recently trying to compute
> intnum(x=0,oo, (sin(x)^4)/(x)^2)
> I only get about 3 digits (the integral evaluates to log(2)). There's probably a neat way to get more digits in this particular instance. What I'm looking for is a reasonably complete account of such methods, for even more complicated integrals in PARI. I have, for instance met the integral
> intnum(x=0,oo, exp(x)*besselj(0,x))
> which doesn't even return an answer. Where can I learn how to evaluate such integrals in GP?
>
> References outside just numerical integration are also welcome.
>
> Thanks,
> Kevin