Question about Numerical Integration  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: Question about Numerical Integration (/thread204557.html) 
Question about Numerical Integration  Namir  11102011 The Integrate function in several HP calculators calculates the integral between two values, say A and B. Are there any tricks to use the same method when integrating between A and infinity, minus infinity and A, and minus infinity and plus infinity? I know there are special types of Gaussian quadrature methods that can handle the above cases. My question is directed at working with the algorithms for finite integrals.
Namir
Re: Question about Numerical Integration  Valentin Albillo  11102011 Quote: The usual trick is to first perform a simple change of variable which will reduce any interval, including infinities at one or both extremes, to any finite interval you care for such as [0,1] or [1,1]. Best regards from V.
Re: Question about Numerical Integration  Lyuka  11102011 Many RF engineers would like the conversion below, s = (z  1) / (z + 1)
that is used to plot various impedance in a Smith chart. Re: Question about Numerical Integration  Namir  11102011 looks like: s = (x^2  1) / (x^2 + 1) is a better transformation, since it is valid for all real values of x.
Namir
Re: Question about Numerical Integration  peacecalc  11102011 Hallo namir, when you need only numerical results, you can also use instead of infinities great/small numbers like +/ 10^6. That's sometimes tricky, shown in the advanced handbook for the 15c.
sincerely Edited: 10 Nov 2011, 11:59 p.m.
Re: Question about Numerical Integration  Namir  11112011 That's the kind of tricks I was looking for. Putting it in pseudocode form in the case of integrating from A to infinity:
Given f(x), A, SmallValue, RelTolerance, and DiffTolerance Here is a perhaps more efficient version that uses integration by parts:
Given f(x), A, SmallValue, RelTolerance, and DiffTolerance
Edited: 11 Nov 2011, 5:47 a.m.
Re: Question about Numerical Integration  Mike (Stgt)  11112011 IIRC, there is a discussion worth to read in the PPCROM manual. Hope this hepls
Ciao.....Mike
Re: Question about Numerical Integration  Gjermund Skailand  11112011 TanhSinh transformation or "Double exponential method" may also be efficient, especially when the function is oscillating. Re: Question about Numerical Integration  Dieter  11112011 As already pointed out, there are basically two approaches for handling improper integrals:
