Post Reply 
Fractional Part - A Difficult Integral
06-30-2014, 01:17 PM
Post: #8
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.
Find all posts by this user
Quote this message in a reply
Post Reply 

Messages In This Thread
RE: Fractional Part - A Difficult Integral - ttw - 06-30-2014 01:17 PM

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