Let be a weight function represented in terms of the moments defined by

where for . Gautschi [8] describes a procedure for the recursive computation of the coefficients and for the three-term recurrence

where the set of polynomials are orthogonal on with respect to the weight function . That is,

Whereas
Gautschi's procedure in [8] is numerically unstable for
computing the recurrence in Equation (14),
a more stable procedure may be obtained if
is codified in terms of the * modified moments*

where is a set of orthogonal polynomials satisfying a recurrence relation of the form

It has been shown in [10] that some simplifications to
this more stable procedure are possible when the polynomials
are chosen to be the Chebyshev polynomials.
The simplified procedure is described in Section
3 as part of the CSI-MSVD algorithm.

Michael W. Berry (berry@cs.utk.edu)

Sun May 19 11:34:27 EDT 1996