orthopolynom (version 1.0-6.1)

polynomial.powers: Create a list of polynomial linear combinations

Description

This function returns a list with \(n + 1\) elements containing the vector of linear combinations of the order \(k\) polynomials for orders \(k = 0,\;1,\; \ldots ,\;n\). Each element in the list is a vector.

Usage

polynomial.powers(polynomials)

Value

A list of \(n + 1\) elements where each element is a vector of linear combinations.

1

Linear combination(s) of polynomials up to order 0

2

Linear combination(s) of polynomials up to order 1

...

n+1

Linear combination(s) of polynomials up to order \(n\)

Arguments

polynomials

A list of polynomials

Author

Frederick Novomestky

Details

The \(j\)-th component in the list is a vector of linear combinations of the order \(k\) polynomials for orders \(k = 0,\;1,\; \ldots ,\;j - 1\) equal to the monomial x raised to the power \(j - 1\).

Examples

###
### generate Legendre polynomials of orders 0 to 10
###
polynomials <- legendre.polynomials( 10 )
###
### generate list of linear combinations of these polynomials
###
alphas <- polynomial.powers( polynomials )
print( alphas )