Generalized block triangular preconditioner for symmetric saddle point problems. (English) Zbl 1184.65035

V. Simoncini [Appl. Numer. Math. 49, No. 1, 63–80 (2004; Zbl 1053.65033)] and on the other hand Z.-H. Cao [Appl. Numer. Math. 57, No. 8, 899–910 (2007; Zbl 1118.65021)] have discussed two block triangular preconditioners for symmetric saddle point problems. By multiplying the given large dimensional matrix with such a preconditioner the performance of iterative methods such as the generalized minimal residual method (GMRES(\(n\))) is improved dramatically. Here by introdducing an additional parameter, the two above mentioned preconditioners are embedded in a family of preconditioners and will so give room for improvements. For the discussion of the expected numerical behaviour regions where the eigenvalues are situated are described. Numerical experiments for such a problem are described in detail.


65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems


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