Inspired by Tikhonov regularization, a non-linear conjugate gradient method is proposed with the purpose of simultaneously regularizing and solving the moment matrix equation. The procedure is based on a non-quadratic conjugate gradient algorithm with exact line search, restart and rescale. Applied to the problem of TM scattering by perfectly conducting rectangular cylinders, the method is show...

Abstract. We propose and study, for structural dynamic problems, a domain decomposition method based on an augmented Lagrangian formulation. This method uses an inexact Uzawa algorithm to solve the linear system required at any time increment. The proposed algorithm is interesting, for parallel and vector applications, because it doesn’t need scalar products and has less operations by iteration...

This paper proposes a line search technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee the descent condition at each iteration of the Polak-Ribière-Polyak conjugate gradient algorithm. It is proved that this line search algorithm preserves the usual convergence properties of any descent algorithm. In particular, it is shown that the Zoutendijk condition holds...

We present a novel linear solver that works well for large systems obtained from discretizing PDEs. It is robust and, for the examples we studied, the computational eeort scales linearly with the number of equations. The algorithm is based on a wavelength decomposition that combines conjugate gradient, multi-scaling and iterative splitting methods into a single approach. On the surface, the alg...

A two-dimensional shape identification problem, i.e. inverse geometry problem, of estimating simultaneously two interfacial configurations in a multiple (three) region domain is solved in this study by using the Conjugate Gradient Method (CGM) and Boundary Element Method (BEM)-based inverse algorithm. Two over-utilized conditions should be applied in determining two gradient equations, this dif...

The smoothing procedure has been introduced by Schh onauer as an acceleration algorithm for the Generalized Conjugate Gradient methods. In this paper, after giving our deenition of Conjugate Gradient type methods, and using a Generalized Hessenberg process, we introduce a Hybrid generalized Conjugate Gradient type method. We show that this Hybrid procedure is a variable smoothing procedure. And...

Conjugate gradient methods are efficient for smooth optimization problems, while there are rare conjugate gradient based methods for solving a possibly nondifferentiable convex minimization problem. In this paper by making full use of inherent properties of Moreau-Yosida regularization and descent property of modified conjugate gradient method we propose a modified Fletcher-Reeves-type method f...

Much is already known about when a conjugate gradient method can be implemented with short recursions for the direction vectors. The work done in 1984 by Faber and Manteuuel 3] gave necessary and suucient conditions on the iteration matrix A, in order for a conjugate gradient method to be implemented with a single recursion of a certain form. However, this form does not take into account all po...

In a recent paper [2] we introduced the greedy Gradient Pursuit framework. This is a family of algorithms designed to find sparse solutions to underdetermined inverse problems. One particularly powerful member of this family is the (approximate) conjugate gradient pursuit algorithm, which was shown to be applicable to very large data sets and which was found to perform nearly as well as the tra...