jacobi.matrices {orthopolynom}

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)

Arguments

r

a data frame containing the parameters a and b

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

Author(s)

Frederick Novomestky [e-mail]

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 )