Galerkin Projection Methods for Solving Multiple 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 ...

Analysis of Projection Methods for Solving Linear Systems with Multiple Right-Hand Sides

We analyze a class of Krylov projection methods but mainly concentrate on a specific conjugate gradient (CG) implementation by Smith, Peterson, and Mittra [IEEE Transactions on Antennas and Propogation, 37 (1989), pp. 1490–1493] to solve the linear system AX = B, where A is symmetric positive definite and B is a multiple of right-hand sides. This method generates a Krylov subspace from a set of...

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...

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