legendre.quadrature.rules {gaussquad} | R Documentation |
Create list of Legendre quadrature rules
Description
This function returns a list with elements containing
the order
quadrature rule data frame for
the Legendre polynomial
for orders
.
Usage
legendre.quadrature.rules(n,normalized=FALSE)
Arguments
n |
integer value for the highest order |
normalized |
boolean value. if TRUE rules are for orthonormal polynomials, otherwise they are for orthgonal polynomials |
Details
An order quadrature data frame is a named data frame that contains
the roots and abscissa values of the corresponding order
orthogonal polynomial.
The column with name
x
contains the roots or zeros and
the column with name w
contains the weights.
Value
A list with $n$ elements each of which is a data frame
1 |
Quadrature rule data frame for the order 1 Legendre polynomial |
2 |
Quadrature rule data frame for the order 2 Legendre polynomial |
...
n |
Quadrature rule data frame for the order $n$ Legendre polynomial |
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Abramowitz and Stegun (1968), Press et. al. (1992)
See Also
Examples
###
### generate a list of quadrature rule frames for
### the orthogonal Legendre polynomials
### of orders 1 to 5
###
orthogonal.rules <- legendre.quadrature.rules( 5 )
print( orthogonal.rules )
###
### generate a list of quadrature rule frames for
### the orthonormal Legendre polynomials
### of orders 1 to 5
###
orthonormal.rules <- legendre.quadrature.rules( 5, TRUE )
print( orthonormal.rules )