An analysis of low-rank modifications of preconditioners for saddle point systems.
An analysis of the composite step biconjugate gradient method.
An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems
This paper extends previous results on nonlinear Schwarz preconditioning (Cai and Keyes 2002) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The nonlocal finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in Jones...
An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation.
An imperfect conjugate gradient algorithm
A new biorthogonalization algorithm is defined which does not depend on the step-size used. The algorithm is suggested so as to minimize the total error after steps if imperfect steps are used. The majority of conjugate gradient algorithms are sensitive to the exactness of the line searches and this phenomenon may destroy the global efficiency of these algorithms.
An incomplete-factorization preconditioning using repeated red-black ordering.
An intoduction to formal orthogonality and some of its applications.
This paper is an introduction to formal orthogonal polynomials and their application to Padé approximation, Krylov subspace methods for the solution of systems of linear equations, and convergence acceleration methods. Some more general formal orthogonal polynomials, and the concept of biorthogonality and its applications are also discussed.
An iterative algorithm for testing solvability of max-min interval systems
This paper is dealing with solvability of interval systems of linear equations in max-min algebra. Max-min algebra is the algebraic structure in which classical addition and multiplication are replaced by and , where . The notation represents an interval system of linear equations, where and are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 and T5 solvability and give necessary and...
An Iterative Method for the Matrix Principal n-th Root
In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.
An iterative method of alternating type for systems with special block matrices
An iterative procedure for systems with matrices originalting from the domain decomposition technique is proposed. The procedure introduces one iteration parameter. The convergence and optimization of the method with respect to the parameter is investigated. The method is intended not as a preconditioner for the CG method but for the independent use.
An Iterative Substructuring Algorithm for Equilibrium Equations.
An Optimal Order Multigrid Method for Biharmonic, C1 Finite Element Equations.
Analysis of multilevel decomposition iterative methods for mixed finite element methods
Analysis of some Krylov subspace methods for normal matrices via approximation theory and convex optimization.
Analysis of the Du Fort-Frankel method for linear systems
Analysis of the Schwarz algorithm for mixed finite elements methods
Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework.
Analysis of two-level domain decomposition preconditioners based on aggregation
In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider a set of assumptions...
Analysis of two-level domain decomposition preconditioners based on aggregation
In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider a...
Applying approximate LU-factorizations as preconditioners in eight iterative methods for solving systems of linear algebraic equations
Many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, either to a system of linear algebraic equations or to a sequence of such systems. The solution of a system of linear algebraic equations is very often the most time-consuming part of the computational process during the treatment of the original problem, because these systems can be very large (containing up to many millions of equations). It is, therefore, important...