On a conjugate gradient-type method for solving complex symmetric linear systems

An Augmented Conjugate Gradient Method for Solving Consecutive Symmetric Positive Definite Linear Systems

Many scientific applications require one to solve successively linear systems Ax = b with different right-hand sides b and a symmetric positive definite matrix A. The conjugate gradient method applied to the first system generates a Krylov subspace which can be efficiently recycled thanks to orthogonal projections in subsequent systems. A modified conjugate gradient method is then applied with ...

A METHOD FOR SOLVING FUZZY LINEAR SYSTEMS

In this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. Also necessary and sufficient conditions for existenceof solution are given. Some numerical examples illustrate the efficiencyof the method.

CG Type Algorithm for Indefinite Linear Systems 1 Conjugate Gradient Type Methods for Solving Symmetric , Inde nite

The conjugate gradient algorithm (CG) is an eeective tool for solving a system of linear equation with a positive deenite coeecient matrix. We show the reasons for a possible breakdown of the method when applied to a symmetric system with an indeenite coeecient matrix. Although in nite arithmetic a breakdown of the method occurs rather seldom, near breakdowns may slow down the speed of converge...

A Three-terms Conjugate Gradient Algorithm for Solving Large-Scale Systems of Nonlinear Equations

Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear e...

Defuzzification method for solving fuzzy linear systems