orthopolynom (version 1.0-4)

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

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