Projection Methods for Solving Sparse Linear Systems

Galerkin Projection Methods for Solving Multiple Linear Systems

In this paper, we consider using Galerkin projection methods for solving multiple linear systems A (i) x (i) = b (i) , for 1 i s, where the coeecient matrices A (i) and the right-hand sides b (i) are diierent in general. In particular, we focus on the seed projection method which generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed ...

Projection Methods for Linear Systems

The aim of this paper is to give a uniied framework for deriving projection methods for solving systems of linear equations. We shall show that all these methods follow from a unique minimization problem. The particular cases of the methods of steepest descent, Richardson and conjugate gradients will be treated in details. Projection acceleration procedures for accelerating the convergence of a...

Solving Sparse Integer Linear Systems

We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a p-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic complexity in terms of machine operations subject to a conjecture on the e ectiveness of certain sparse projections. A LinBox based implementation of this algorithm ...

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.

Defuzzification method for solving fuzzy linear systems