As discussed in [10], the basic iteration
can be used to solve the system of linear equations
where M is either the 
matrix 
or the 
matrix defined by Equation (2). Also
assume that the matrix
M is suitably scaled so that its spectral radius (
) is less than
1. If the Chebyshev semi-iterative method [13] is
used to solve systems defined by Equation (4),
the iteration in Equation
(3) will be of the form
where 
is a polynomial of degree k in M, and 
is
a column vector of dimension 
or 
depending on
whether M is the two-cyclic matrix of Equation (2) or the
matrix 
. In this section, a procedure (CSI-MSVD) for estimating
the eigenvalues
of M (corresponding to the largest singular values of A) using
Equation (5) with the method of modified
moments is discussed. A more formal review of the theory of iterative methods
which addresses
issues such as convergence criteria and rates of
convergence to establish the optimality of the Chebyshev semi-iterative
method is given in [22]. In succeeding sections,
will be taken to indicate the Euclidean norm, unless stated otherwise.
