Fractional Part  A Difficult Integral

06302014, 01:17 PM
Post: #8




RE: Fractional Part  A Difficult Integral
Numerical integration of things like Frac(x)dx do not gain by using highorder 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 (2j1)/2N for j=1,N as an Npoint 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  06292014, 11:36 AM
RE: Fractional Part  A Difficult Integral  Massimo Gnerucci  06292014, 11:55 AM
RE: Fractional Part  A Difficult Integral  pito  06292014, 05:18 PM
RE: Fractional Part  A Difficult Integral  kakima  06292014, 06:17 PM
RE: Fractional Part  A Difficult Integral  Gerald H  06292014, 07:57 PM
RE: Fractional Part  A Difficult Integral  Thomas Klemm  06292014, 06:47 PM
RE: Fractional Part  A Difficult Integral  pito  06292014, 09:40 PM
RE: Fractional Part  A Difficult Integral  ttw  06302014 01:17 PM

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