Toward the reusability for iterative linear algebra software in distributed environment

Abstract

LAKe (Linear Algebra Kernel) is a linear algebra class library developed using an object oriented approach in order to enable a good reuse code for sequential or parallel linear algebra applications. An application implemented using LAKe can be run either in sequential or in parallel mode using the same code. This paper proposes an extension to the LAKe library, which enables an implemented method to run in sequential and parallel mode simultaneously. This extension of LAKe allows a concurrent reuse of sequential and parallel components inside the same linear algebra application. To take advantage of such concurrent reusability, the sequential and parallel components have to be able to collaborate with each other. The hybrid methods need such properties to run. These methods are defined by a combination of several numerical techniques, or several copies of the same method parameterized differently in order to accelerate the convergence and/or to improve the accuracy of the solution of a given large linear algebra problem. In order to validate our approach, we present some numerical experiments, making use of a hybrid method with the proposed extension of LAKe.