We present a method for the computation of stopping criterion for linear classical iterations in inexact aane-invariant Newton techniques. We show that the same methodology does not hold for non-classical iterative methods.

Based on the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four-parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the ...

This work presents computational strategies used in an implementation of the probabilistic discrete cracking model for concrete of Rossi suitable to parallel vector processor (PVP). The computational strategies used for each realization, within the framework of Monte Carlo simulation, are the inexact Newton method to solve the highly nonlinear problem and element-by-element (EBE) iterative stra...

We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspacemethods.We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding preconditi...

Edge-based data structures are used to improve computational efficiency of Inexact Newton methods for solving finite element nonlinear solid mechanics problems on unstructured meshes. Edge-based data structures are employed to store the stiffness matrix coefficients and to compute sparse matrix-vector products needed in the inner iterative driver of the Inexact Newton method. Numerical experime...

In this paper we study the global convergence behavior of a class of composite–step trust–region SQP methods that allow inexact problem information. The inexact problem information can result from iterative linear systems solves within the trust–region SQP method or from approximations of first–order derivatives. Accuracy requirements in our trust– region SQP methods are adjusted based on feasi...

In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results ...

where F (ξ) is a nonlinear operator from a real Euclidean space of dimension n or Hilbert space into itself. The Euclidean norm and corresponding inner product will be denoted by ‖·‖1 and (·, ·)1 respectively. A general different inner product with a weight function and the corresponding norm will be denoted by (·, ·)0 and ‖ · ‖ respectively. In the first part of this article (Sects. 2 and 3) w...

The paper presents a semismooth inexact Newton-type method for solving optimal power flow (OPF) problem. By introducing the nonlinear complementarity problem (NCP) function, the Karush-KuhnTucker (KKT) conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by an improved inexact LevenbergMar...

The computation of a right eigenvector and corresponding finite eigenvalue of a large sparse generalised eigenproblem Ax = λMx using preconditioned Rayleigh quotient iteration and the simplified JacobiDavidson method is considered. Both methods are inner-outer iterative methods and we consider GMRES and FOM as iterative algorithms for the (inexact) solution of the inner systems that arise. The ...