gaussquad (version 1.0-3)

jacobi.g.quadrature.rules: Create list of Jacobi quadrature rules

Description

This function returns a list with \(n\) elements containing the order \(k\) quadrature rule data frame for the Jacobi G polynomial for orders \(k = 1,\;2,\; \ldots ,\;n\).

Usage

jacobi.g.quadrature.rules(n,p,q,normalized=FALSE)

Arguments

n

integer value for the highest order

p

numeric value for the first polynomial parameter

q

numeric value for the second polynomial parameter

normalized

boolean value. if TRUE rules are for orthonormal polynomials, otherwise they are for orthgonal polynomials

Value

A list with \(n\) elements each of which is a data frame

1

Quadrature rule data frame for the order 1 Jacobi polynomial

2

Quadrature rule data frame for the order 2 Jacobi polynomial

...

n

Quadrature rule data frame for the order \(n\) Jacobi polynomial

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.

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

Examples

# NOT RUN {
###
### generate the list of quadrature rule data frames for
### the orthogonal Jacobi G polynomial
### of orders 1 to 5
### parameter p is 3 and parameter q is 2
###
orthogonal.rules <- jacobi.g.quadrature.rules( 5, 3, 2 )
print( orthogonal.rules )
###
### generate the list of quadrature rule data frames for
### the orthonormal Jacobi G polynomial
### of orders 1 to 5
### parameter p is 3 and parameter q is 2
###
orthonormal.rules <- jacobi.g.quadrature.rules( 5, 3, 2, TRUE )
print( orthonormal.rules )
# }