An Augmented Conjugate Gradient Method for Solving Consecutive Symmetric Positive Definite 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 ...

Conjugate gradient method for fuzzy symmetric positive definite system of linear equations

In this paper the conjugate gradient method, for solving fuzzy symmetric positive definite system of linear equation is considered. The method in detail is discussed and followed by convergence theorem and illustrated by solving some numerical examples. 2005 Elsevier Inc. All rights reserved.

Parallel Numerical Algorithms for Symmetric Positive Definite Linear Systems

We give a matrix factorization for the solution of the linear system Ax = f , when coefficient matrix A is a dense symmetric positive definite matrix. We call this factorization as "WW T factorization". The algorithm for this factorization is given. Existence and backward error analysis of the method are given. The WDWT factorization is also presented. When the coefficient matrix is a symmetric...

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