quadrature.rules: Create a list of quadrature rule data frames

In gaussquad: Collection of Functions for Gaussian Quadrature

Create a list of quadrature rule data frames

Description

This function returns a list with n elements containing the order $k$ quadrature rule data frames for orders k = 1,\;2,\; … ,\;n.

Usage

quadrature.rules(recurrences, inner.products)

Arguments

recurrences	a data frame with the recurrence parameters of a particular orthogonal polynomial
inner.products	a numeric vector of normed squared values of the orthogonal polynomials

Details

An order k quadrature data frame is a named data frame that contains the roots and abscissa values for the quadrature rule based on an order k orthgonal polynomial.

Value

A list with n elements each of which is a quadrature rule data frame

1	Quadrature rule for the order 1 orthogonal polynomial
2	Quadrature rule for the order 2 orthogonal polynomial

...

n	Quadrature rule for the order n orthogonal polynomial

Author(s)

Frederick Novomestky [e-mail]

References

Abramwitz and Stegun (1968)

Examples

###
### get recurrences the Chebyshev T orthgonal polynomials
### of orders 0 to 6\5
###
recurrences <- chebyshev.t.recurrences( 5 )
###
### get the inner products of these polynomials
###
inner.products <- chebyshev.t.inner.products( 5 )
###
### get the quadrature rules
###
rules <- quadrature.rules( recurrences, inner.products )
print( rules )

gaussquad documentation built on June 14, 2022, 9:05 a.m.