In this paper we give the results found in solving consistent sparse systems of nonlinear equations by an inexact Newton and Quasi-Newton method both combined with a block iterative row-projection linear solver of Cimmino-type. A simple partitioning of the Jacobian matrix was used for solving two nonlinear test problems, that is a tridiagonal problem of size n = 131072 and a nonlinear Poisson p...

Certain implicit time stepping procedures for the incompressible Stokes or Navier-Stokes equations lead to a singular-perturbed Stokes type problem at each type step. The paper presents a convergence analysis of a geometric multigrid solver for the system of linear algebraic equations resulting from the disretization of the problem using a finite element method. Several smoothing iterative meth...

We introduce in this paper a new class of nonlinear operators which contains, among others, the class of operators with semimonotone additive inverse and also the class of nonexpansive mappings. We study this class and discuss some of its properties. Then we present iterative procedures for computing fixed points of operators in this class, which allow for inexact solutions of the subproblems a...

For the Hermitian inexact Rayleigh quotient iteration (RQI), we present general convergence results, independent of iterative solvers for inner linear systems. We prove that the method converges quadratically at least under a new condition, called the uniform positiveness condition. This condition can be much weaker than the commonly used one that at outer iteration k, requires the relative res...

In this paper we present the results obtained in the solution of sparse and large systems of nonlinear equations by Inexact Newton-like methods [6]. The linearized systems are solved with two preconditioners particularly suited for parallel computation. We report the results for the solution of some nonlinear problems on the CRAY T3E under the MPI environment. Our methods may be used to solve m...

This paper makes two contributions to the area of single-word based word alignment for bilingual sentence pairs. Firstly, it integrates the – seemingly rather different – works of (Bodrumlu et al., 2009) and the standard probabilistic ones into a single framework. Secondly, we present two algorithms to optimize the arising task. The first is an iterative scheme similar to Viterbi training, able...

We review the use of block diagonal and block lower/upper triangular splittings for constructing iterative methods and preconditioners for solving stabilized saddle point problems. We introduce new variants of these splittings and obtain new results on the convergence of the associated stationary iterations and new bounds on the eigenvalues of the corresponding preconditioned matrices. We furth...

The Boundary Element Tearing and Interconnecting (BETI) methods have recently been introduced as boundary element counterparts of the well–established Finite Element Tearing and Interconnecting (FETI) methods. In this paper we present inexact data–sparse versions of the BETI methods which avoid the elimination of the primal unknowns and dense matrices. However, instead of symmetric and positive...

A flexible version of the QMR algorithm is presented which allows for the use of a different preconditioner at each step of the algorithm. In particular, inexact solutions of the preconditioned equations are allowed, as well as the use of an (inner) iterative method as a preconditioner. Several theorems are presented relating the norm of the residual of the new method with the norm of the resid...

We review optimization models for congestion control, focusing on the dual of a widely studied utility maximization problem. We show that many congestion control algorithms can be modeled within this framework, and conversely, standard techniques for iterative optimization can inspire practical congestion control algorithms. This previous work all assumes precise feedback of congestion informat...