Fractional Part - A Difficult Integral
06-30-2014, 01:17 PM
Post: #8
 ttw Member Posts: 194 Joined: Jun 2014
RE: Fractional Part - A Difficult Integral
Numerical integration of things like Frac(x)dx do not gain by using high-order rules (Simpson's, Gauss, etc.) because the first derivative is not continuous.

Monte Carlo (and quasi Monte Carlo) does no worse than its usual performance (which isn't that good anyway) as the variance (or variation) is small.

One QMC example is to use the points (2j-1)/2N for j=1,N as an N-point integration formula. Another is to use Frac(N*Sqrt(2)) as a sequence to integrate these types of functions.

The last sequence is easy to compute; just add Frac(Sqrt(2)) at each step and reduce below 1.
 « Next Oldest | Next Newest »

 Messages In This Thread Fractional Part - A Difficult Integral - Gerald H - 06-29-2014, 11:36 AM RE: Fractional Part - A Difficult Integral - Massimo Gnerucci - 06-29-2014, 11:55 AM RE: Fractional Part - A Difficult Integral - pito - 06-29-2014, 05:18 PM RE: Fractional Part - A Difficult Integral - kakima - 06-29-2014, 06:17 PM RE: Fractional Part - A Difficult Integral - Gerald H - 06-29-2014, 07:57 PM RE: Fractional Part - A Difficult Integral - Thomas Klemm - 06-29-2014, 06:47 PM RE: Fractional Part - A Difficult Integral - pito - 06-29-2014, 09:40 PM RE: Fractional Part - A Difficult Integral - ttw - 06-30-2014 01:17 PM

User(s) browsing this thread: 1 Guest(s)