polynomial.roots {orthopolynom} | R Documentation |
This function returns a list with $n$ elements containing the roots of the order $k$ monic orthogonal polynomials for orders $k$ = 1, ... , $n$ using a data frame with the monic polynomial recurrence parameter vectors bf{a} and bf{b}
polynomial.roots(m.r)
m.r |
monic recurrence data frame with parameters a and b |
The parameter m.r
is a data frame with $n$+1 rows and two names columns. The columns which are names a
and b
correspond to the above referenced vectors.
Function jacobi.matrices
is used to create a list of symmetric, tridiagonal Jacobi matrices from these named columns. The eigenvalues of the k times k Jacobi matrix are the roots or zeros of the order $k$ monic orthogonal polynomial.
A list with n elements each of which is a vector of polynomial roots
1 |
roots of the order 1 monic polynomial |
2 |
roots of the order 2 monic polynomial |
n |
roots of the order $n$ monic polynomial |
Frederick Novomestky fnovomes@poly.edu
Press, et. al. (1992)
monic.polynomial.recurrences
jacobi.matrices
,
eigen
r <- chebyshev.t.recurrences( 10, normalized=TRUE ) m.r <- monic.polynomial.recurrences( r ) p.roots <- polynomial.roots( m.r )