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...

The boundary element method has become a popular tool for the solution of Maxwell’s equations in electromagnetism. From a linear algebra point of view, this leads to the solution of large dense complex linear systems where the unknowns are associated with the edges of the mesh defined on the surface of the illuminated object. In this paper, we address the iterative solution of these linear syst...

Block lower triangular and block upper triangular matrices are popular preconditioners for nonsymmetric saddle point matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned systems are related. Nonsingular saddle point matrices of the form

In this paper, we study an efficient tridiagonal preconditioner, based on numerical differentiation, applied to the matrix-free truncated Newton method for unconstrained optimization. It is proved that this preconditioner is positive definite for many practical problems. The efficiency of the resulting matrix-free truncated Newton method is demonstrated by results of extensive numerical experim...