In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we can apply these strategies to Inexact Newton Interior–Point method and we present some numerical ex...

Title of dissertation: NUMERICAL SOLUTION OF EIGENVALUE PROBLEMS WITH SPECTRAL TRANSFORMATIONS Fei Xue, Doctor of Philosophy, 2009 Dissertation directed by: Professor Howard C. Elman Department of Computer Science Institute for Advanced Computer Studies This thesis is concerned with inexact eigenvalue algorithms for solving large and sparse algebraic eigenvalue problems with spectral transforma...

Inexact Krylov subspace methods have been shown to be practical alternatives for the solution of certain linear systems of equations. In this paper, the solution of singular systems with inexact matrix-vector products is explored. Criteria are developed to prescribe how inexact the matrix-vector products can be, so that the computed residual remains close to the true residual, thus making the i...

This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how material and radiation energy coupled, which determines number of iterations needed to converge emission source, diffusion equation is solved, must be done each iteration. The coupled equations solved using an inexact Newton it...

We study inexact Rayleigh quotient iteration (IRQI) for computing a simple interior eigenpair of the generalized eigenvalue problem Av = λBv, providing new insights into a special type of preconditioners with “tuning” for the efficient iterative solution of the shifted linear systems that arise in this algorithm. We first give a new convergence analysis of IRQI, showing that locally cubic and q...

There are classes of linear problems for which the matrix-vector product is a time consuming operation because an expensive approximation method is required to compute it to a given accuracy. In recent years different authors have investigated the use of, what is called, relaxation strategies for various Krylov subspace methods. These relaxation strategies aim to minimize the amount of work tha...

in the present study, water allocation of latian dam between agricultural products was evaluated by using inexact two-stage optimization model and the final results were compared to a fuzzy interval. data were collected from the regional water and agricultural organization of tehran province for 1991 to 2009 years. the results showed that by using interval fuzzy programming, 63%, 69%, 49% and 3...