Local convergence of the
(exact and inexact) iterative aggregation method for linear systems and Markov operators |
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Authors: | Ivo Marek Daniel B Szyld |
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Institution: | (1) Katedra Numerick\'{e} Matematiky, Matematicko-Fyzik\'{a}ln\'{\i} Fakulta, Univerzita Karlova, Malostransk\'{e} n\'{a}m. 12, 118 00 Praha 1, Czech Republic; marek{\tt @}cspguk11.bitnet , CS;(2) Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122-2585, USA; szyld{\tt @}math.temple.edu , US |
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Abstract: | Summary. The iterative aggregation method
for the solution of linear systems is
extended in several directions:
to operators on Banach spaces; to the method with inexact correction, i.e.,
to methods where the (inner) linear system is in turn solved
iteratively; and to the problem of finding
stationary distributions of Markov operators.
Local convergence is shown in all cases.
Convergence results apply to the particular case of stochastic
matrices. Moreover, an argument is given which suggests why the
iterative aggregation method works so well for nearly
uncoupled Markov chains, as well as for Markov chains with
other zero-nonzero structures.
Received
May 25, 1991/Revised version received February 23, 1994 |
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Keywords: | Mathematics Subject Classification (1991): 65F10 65F15 65J10 15A48 15A06 46A22 90A15 |
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