ELA, Volume 9, pp. 55-66, May 2002, abstract.
The convergence rate of the chebyshev
semiiterative method under a perturbation
of the foci of an elliptic domain
Xiezhang Li and Fangjun Arroyo
The Chebyshev semiiterative method (CHSIM)
is a powerful method for finding the iterative
solution of a nonsymmetric real linear system
Ax=b if an ellipse excluding the origin well
fits the spectrum of A. The asymptotic rate
of convergence of the CHSIM for solving the above
system under a perturbation of the foci of the
optimal ellipse is studied. Several formulae to
approximate the asymptotic rates of convergence,
up to the first order of a perturbation, are
derived. These generalize the results about the
sensitivity of the asymptotic rate of convergence
to a perturbation of a real-line segment spectrum
by Hageman and Young, and by the first author.
A numerical example is given to illustrate
the theoretical results.