For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves soluti...

This paper presents an efficient preconditioner for the Lippmann-Schwinger equation that combines the ideas of the sparsifying and the sweeping preconditioners. Following first the idea of the sparsifying preconditioner, this new preconditioner starts by transforming the dense linear system of the Lippmann-Schwinger equation into a nearly sparse system. The key novelty is a newly designed perfe...

We study the high-contrast biharmonic plate equation with HCT and Morley discretizations. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by Aksoylu et al. (2008, Comput. Vis. Sci. 11, pp. 319–331). By extending the devised singular perturbation analysis from linear finite element discretization to the ...

We propose a modified alternating positive semidefinite splitting (MAPSS) preconditioner for solving block three-by-three saddle point problems that arise in linear programming and the finite element discretization of Maxwell equations. Spectral properties MAPSS-preconditioned matrix are discussed analyzed detail. As efficiency MAPSS depends on its parameters, we derive fast effective formulas ...

A method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix A is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations. It is proved that in exact arithmetic the preconditioner is well defined if A is an H-matrix. The results of numerical experiments are pre...

Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed at each iteration step by a suitable approximation process, e.g., by GMRES itself.

For the solution of symmetric linear systems using an iterative method with SSOR preconditioning, we introduce a shift parameter to the preconditioner which can provide improved convergence behaviour. We construct some test cases to explore the properties of the shifted SSOR preconditioner. Linear systems from an actual industrial application are used to demonstrate the improved performance cha...

Linear system with M-matrices often appear in a wide variety of areas. In this work, we propose a new preconditioner for solving the system with nonsingular M-matrix. We show that our preconditioner increases the convergence rate of basic iterative methods. We also give a comparison between preconditioners with different parameters. Numerical results are also given.

A domain decomposition method based on a simple change of basis on the interfaces and vertices is presented. It is shown that this leads to an effective preconditioner compared to the ones previously considered, such as the preconditioner by Bramble, Pasciak, and Schatz (BPS) [Math. Comp., 47 (1986), pp. 103-134], and the hierarchical basis domain decomposition (HBDD) preconditioner by Smith an...