Biconjugate Gradient Method for Sparse Linear Systems

An Analysis of the Composite Step Biconjugate Gradient Method

The composite step biconjugate gradient method (CSBCG) is a simple modification of the standard biconjugate gradient algorithm (BCG) which smooths the sometimes erratic convergence of BCG by computing only a subset of the iterates. We show that 2 × 2 composite steps can cure breakdowns in the biconjugate gradient method caused by (near) singularity of principal submatrices of the tridiagonal ma...

Analysis of the finite precision s-step biconjugate gradient method

We analyze the s-step biconjugate gradient algorithm in finite precision arithmetic and derive a bound for the residual norm in terms of a minimum polynomial of a perturbed matrix multiplied by an amplification factor. Our bound enables comparison of s-step and classical biconjugate gradient in terms of amplification factors. Our results show that for s-step biconjugate gradient, the amplificat...

A Parallel Implementation of the Communication-Avoiding Biconjugate Gradient Method

The speed of an algorithm is determined by two factors: the number of oating-point operations performed (computation) and the amount of data movement (communication). In the sequential case, communication refers to movement of data between levels of the memory hierarchy. In the parallel case, communication means movement of data between processors. Communication cost can be modeled by two param...

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