Create a list of quadrature rule data frames

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Description

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

Usage

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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 fnovomes@poly.edu

References

Abramwitz and Stegun (1968)

Examples

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###
### 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 )

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