Generate the quadrature rule table

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Description

This function returns a column-named data frame with the given quadrature rules combined into a single object

Usage

1

Arguments

rules

A list of quadrature rule data frames

Details

The column-named data frame has four columns. The first column is called d and it contains the degree of the orthogonal polynomial. The second column is called i and it contains the index of the rule for the given polynomial order. The third column is called x and it contains the abscissas, roots or zeros of the polynomial of given order. The fourth column is called w and it contains the weights associated with the abscissas.

Value

A data frame with the quadrature rules.

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

Examples

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###
### generate the list of quadrature rules for
### the Chebyshev T polynomials
### of orders 1 to 5
###
rules <- chebyshev.t.quadrature.rules( 5 )
###
### construct the rule table
###
rule.table <- quadrature.rule.table( rules )
print( rule.table )

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