Volume 7, pp. 40-55, 1998.
Convergence analysis of an inexact truncated RQ-iteration
Chao Yang
Abstract
The Truncated RQ-iteration (TRQ) can be used to calculate interior
or clustered eigenvalues of a large sparse and/or structured matrix
. This method requires solving a sequence of linear equations.
When these equations can be solved accurately by a direct
solver, the convergence of each eigenvalue is quadratic in general
and cubic if is hermitian. An important question is whether
the TRQ iteration will still converge if these equations are
approximately solved by a preconditioned iterative solver. If it
does converge, how fast is the convergence rate? In this paper,
we analyze the convergence of an inexact TRQ iteration in which
linear systems are solved iteratively with some error. We show
that under some appropriate conditions, the convergence rate of the
inexact TRQ is at least linear with a small convergence factor.
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BibTeX
Key words
Arnoldi method, Lanczos method, eigenvalues, Truncated RQ-iteration.
AMS subject classifications
65F15, 65G05.
