Syntax

C#
[SerializableAttribute] public class HyperRectangleQuadrature

Visual Basic (Declaration)
<SerializableAttribute> _ Public Class HyperRectangleQuadrature

Visual C++
[SerializableAttribute] public ref class HyperRectangleQuadrature

Remarks

This class is used to evaluate integrals of the form:

$\int_{a_{n-1}}^{b_{n-1}} \cdots \int_{a_0}^{b_0} f(x_0,\ldots,x_{n-1}) \, dx_0 \ldots dx_{n-1}$

Integration of functions over hypercubes by Monte Carlo, in which the integral is evaluated as the value of the function averaged over a sequence of randomly chosen points. Under mild assumptions on the function, this method will converge like $1 / \sqrt{n}$ , where n is the number of points at which the function is evaluated.

It is possible to improve on the performance of Monte Carlo by carefully choosing the points at which the function is to be evaluated. Randomly distributed points tend to be non-uniformly distributed. The alternative to a sequence of random points is a low-discrepancy sequence. A low-discrepancy sequence is one that is highly uniform.

This function is based on the low-discrepancy Faure sequence as computed by FaureSequence.

Inheritance Hierarchy

System..::.Object
Imsl.Math..::.HyperRectangleQuadrature

Syntax

Remarks

Inheritance Hierarchy

See Also