| gegenbauer.quadrature.rules {gaussquad} | R Documentation |
Create list of Gegenbauer quadrature rules
Description
This function returns a list with n elements containing
the order k quadrature rule data frame for
the Gegenbauer polynomials
for orders k = 1,\;2,\; \ldots ,\;n.
Usage
gegenbauer.quadrature.rules(n,alpha,normalized=FALSE)
Arguments
n |
integer value for the highest order |
alpha |
polynomial parameter |
normalized |
boolean value. if TRUE rules are for orthonormal polynomials, otherwise they are for orthgonal polynomials |
Details
An order k quadrature data frame is a named data frame that contains
the roots and abscissa values of the corresponding order k 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 Gegenbauer polynomial |
2 |
Quadrature rule data frame for the order 2 Gegenbauer polynomial |
...
n |
Quadrature rule data frame for the order |
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Abramowitz, M. and I. A. Stegun, 1968. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992. Numerical Recipes in C, Cambridge University Press, Cambridge, U.K.
Stroud, A. H., and D. Secrest, 1966. Gaussian Quadrature Formulas, Prentice-Hall, Englewood Cliffs, NJ.
See Also
quadrature.rules,
gegenbauer.quadrature
Examples
###
### generate the list of quadrature rule data frames for
### the orthogonal Gegenbauer polynomials
### of orders 1 to 5
### polynomial parameter alpha is 1.0
###
orthogonal.rules <- gegenbauer.quadrature.rules( 5, 1 )
print( orthogonal.rules )
###
### generate the list of quadrature rule data frames for
### the orthonormal Gegenbauer polynomials
### of orders 1 to 5
### polynomial parameter alpha is 1.0
###
orthonormal.rules <- gegenbauer.quadrature.rules( 5, 1, TRUE )
print( orthonormal.rules )