orthopolynom (version 1.0-5)

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)

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

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

# NOT RUN {
r <- chebyshev.t.recurrences( 5 )
m.r <- monic.polynomial.recurrences( r )
j.m <- jacobi.matrices( m.r )
# }