GaussQuadrature {tdist}R Documentation

Gaussian quadrature weights

Description

The grule computes Gauss base points and weight factors for Gaussian quadrature on interval [0 1] and the gweights is the generator of points and weight factors for the Gaussian quadrature on several different subintervals.

Usage

grule(n)
gweights(limits, ms, bp, wf)

Arguments

n number of base points and weight factors
limits borders of subintervals.
ms number of base points in particular subinterval.
bp base points of the Gaussian quadrature genterated by grule on interval [0 1].
wf weight factors of the Gaussian quadrature genterated by grule on interval [0 1].

Details

The gweights divides the whole interval into ms[i] subintervals given by limits[i] and limits[i + 1] and the integration over each subinterval is done with an nquad point Gauss formula which involves base points BP and weight factors WF. The normalized interval of integration for the BP and WF constants is 0 to 1. The base points and weight factors must first be generated by a call to grule.

Value

The grule generates a list of

bp base points on interval [0 1].
wf weight factors on interval [0 1].
tt base points of all subintervals.
w weight factors of all subintervals.

Author(s)

Gordon K Smyth, STATBOX 4.1 smyth@wehi.edu.au. Rewritten from Matlab algorithm to R by Alexander Savin savin@savba.sk.

References

Davis, Rabinowitz (1975), Methods of Numerical Integration. Academic Press, page 365.


[Package tdist version 0.1-1.1 Index]