Saddle-Point Problems and Their Iterative Solution by Miroslav Rozložník

Author:Miroslav Rozložník
Language: eng
Format: epub, pdf
ISBN: 9783030014315
Publisher: Springer International Publishing

(6.48)

If and are constants independent of the matrix dimension, then the bound for the convergence rate of preconditioned GMRES will not be dependent on this dimension. In addition, if is close to , then a fast convergence of GMRES can be expected. This approach is mainly used for inexact versions of block-diagonal or block-triangular preconditioners, where one of their diagonal blocks is negative definite. Another possible approach is based on the analysis of a degree of the minimal polynomial for the matrix . It appears that this degree can be sometimes very small (it can be even equal to 2 or 3). Then one can expect that every Krylov subspace method will terminate within this (small) number of steps. This property holds for the so-called “exact” versions of block-diagonal or block-triangular preconditioners, or with some modification also for the constraint preconditioner, which will be discussed in next chapter.

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