polynomial.powers {orthopolynom}

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)

Arguments

polynomials

A list of polynomials

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.

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

Author(s)

Frederick Novomestky [e-mail]

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 )