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Keiichi Morikuni - Inner-iteration preconditioning for singular linear systems

Date: 06/01/2015 14:00
Place: Seminární místnost KNM
For solving large sparse linear systems of equations, iterative methods
are preferred in terms of efficiency and memory requirement. When the
problem is ill-conditioned, the convergence of iterative methods tends to
be slow and the convergence may be accelerated by preconditioning.
However, in the singular case, iterative methods and preconditioners may
fail to converge and break down. We give a necessary and sufficient
condition under which the generalized minimal residual (GMRES) method
finds a solution of linear systems of equations with an arbitrary index
without breakdown and characterize the solution. Next, we apply this
result to GMRES preconditioned by several steps of a stationary iterative
method performed as inner iterations, and present theoretical
justifications for using this method and classes of stationary iterative
methods that can be used for inner-iteration preconditioning.