Quadrature Rules Using Halton Points

QUADRATURE_RULES_HALTON is a dataset directory which contains examples of "quadrature rules" based on multidimensional quasirandom Halton sequences.

A quadrature rule is a set of n points x and associated weights w so that the integral of a function f(x) over some particular region can be approximated by:

Integral f(x) dx = Sum ( 1 <= i <= n ) w(i) * f(x(i))

Using a random, pseudorandom, or quasirandom sequence can be regarded as a kind of quadrature rule in which the weight vector is 1/N.

For this directory, a quadrature rule is stored as three files, containing the weights, the points, and a file containing two points defining the corners of the rectangular region. The dimension of the region is deduced implicitly from the dimension of the points.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

HALTON, a C++ library which computes elements of a Halton quasirandom sequence.

INT_EXACTNESS, a C++ program which checks the polynomial exactness of a 1-dimensional quadrature rule for a finite interval.

Sample Files:

HALTON (quasirandom) Quadrature Rules in 6D, defined on the [0,1] square: (we're regarding the method as a sort of quadrature rule with all weights equal)

"HALTON" (quasirandom) Quadrature Rules in 10D, defined on the [0,1] square: (we're regarding the QuasiMonte Carlo method as a sort of quadrature rule with all weights equal)

You can go up one level to the DATASETS page.

Last revised on 10 September 2007.