In this paper, the multilevel ILU (MLILU) decomposition is introduced. During an incomplete Gaussian elimination process new matrix entries are generated such that a special ordering strategy yields distinct levels. On these levels, some smoothing steps are computed. The MLILU decomposition exists and the corresponding iterative scheme converges for all symmetric and positive deenite matrices. ...

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

Standard preconditioners, such as ILU factorizations, often break down in construction for KKT matrices. We compare several approaches for preconditioning KKT systems. The first applies a constraint preconditioner by incorporating robust factored approximations of (BB ) and BB , where B is the (2,1) block of the KKT matrix. In the second approach, we apply permutations and scalings that maximiz...

In this paper we discuss preconditioners for the incompressible Navier-Stokes equations. In combination with Krylov subspace methods, they give a fast convergence for the solution of the Navier -Stokes equations. With the help of numerical experiments, we report some new findings regarding the convergence of these preconditioners. Besides that, a renumbering scheme for direct solvers and ILU pr...

We make a theoretical analysis of the application of the generalized hierarchical basis multigrid method to the convection-diiusion equation, discretized using the Scharfetter-Gummel discretization. Our analysis is performed for two levels of grid reenement in which we compare the eeects of diierent interpolation factors for the coarse grid basis functions on the method. In particular, we nd th...

We present a new method for the a priori approximation of the order of magnitude of the entries in the LU factors of a matrix A ∈ Cn×n. We are also able to predict which permutation matrices will be chosen by partial pivoting or complete pivoting Gaussian elimination. Our method uses maxplus algebra and is based purely on the modulii of the entries in the matrix. This approximation can be used ...