One can also use *polynomial acceleration*
to speed up the
computation by replacing the power by a
polynomial
, in which
is the Chebyshev polynomial of the first kind of degree
, and and give a translation and scaling of the
part of the spectrum one wants to suppress. Ideally one should
take
as the center and
as the half-width of the
interval containing the eigenvalues that are *not*
of interest for some reasonable estimates
of those eigenvalues. We assume that the eigenvalues are
ordered along the real axis and that we want of them in one of the ends.

With these enhancements, subspace iteration may be a reasonably efficient method that has the advantage of being easy to code and to understand. Some of the methods to be discussed later are often preferred, however, because they tend to find eigenvalues/eigenvectors more quickly.

Much of the material in this section is drawn from Demmel [114], Golub and Van Loan [198], and Saad [387]. For further discussion on subspace iteration, the reader is recommended to refer to Chatelin [79], Lehoucq and Scott [292], Stewart [422], and Wilkinson [457]. See also Bathe and Wilson [42] and Jennings [242] for structural engineering approaches.