orthopolynom (version 1.0-6.1)

jacobi.matrices: Create list of Jacobi matrices from monic recurrence parameters

Description

Return a list of $n$ real symmetric, tri-diagonal matrices which are the principal minors of the \(n \times n\) Jacobi matrix derived from the monic recurrence parameters, \(a\) and \(b\), for orthogonal polynomials.

Usage

jacobi.matrices(r)

Value

A list of symmetric, tri-diagnonal matrices

1

a \(1 \times 1\) matrix

2

a \(2 \times 2\) matrix

...

n

an \(n \times n\) matrix

Arguments

r

a data frame containing the parameters \(a\) and \(b\)

Author

Frederick Novomestky

References

Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992. Numerical Recipes in C, Cambridge University Press, Cambridge, U.K.

Examples

r <- chebyshev.t.recurrences( 5 )
m.r <- monic.polynomial.recurrences( r )
j.m <- jacobi.matrices( m.r )