HyperRectangleQuadrature Class

HyperRectangleQuadrature integrates a function over a hypercube.

For a list of all members of this type, see HyperRectangleQuadrature Members.

System.Object
Imsl.Math.HyperRectangleQuadrature

public class HyperRectangleQuadrature

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

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.

Requirements

Namespace: Imsl.Math

Assembly: ImslCS (in ImslCS.dll)

HyperRectangleQuadrature Class

Thread Safety

Remarks

Requirements

See Also