be a weight function codified in terms of the 2n
modified moments 
as defined in Equations
(21) and (22). A procedure to compute
the coefficients of polynomials 
orthogonal with respect
to 
is desired.
From Equation (14), the polynomials
are of the form
Following [10] with the choice 
,
the coefficients 
and 
may be determined using
the recurrences below.
For  , |
|
For  ,
|
Here, 
and 
are defined by Equation (23),
and initially,
The computation of 
's and 
's , 
effectively constructs the elements of the Jacobi matrix from Equation
(17), whose eigenvalues approximate those of
the iteration matrix M.
Thus, by setting M to either of the two canonical matrices described in
Section 1.2,
one can approximate singular triplets of a general matrix by solving
an equivalent symmetric eigenvalue problem. One implementation of this
method (referred to as CSI-MSVD) was first considered in [2]. A
more complete discussion of the method
for each of the canonical eigenvalue problems from
Section 1.2 is given in [22].
