Implementation And Performance Assessment
Of A Parallel Solver For Sparse Linear Systems Of
Equations And Rules For Optimal Solution
Author(s)
T. Grytsenko & A. Peratta
Abstract
Many computational algorithms in science and engineering give rise to large
sparse linear systems of equations which need to be solved as efficiently as
possible. As the size of the problems of interest increases, it becomes necessary
to consider exploiting multiprocessors to solve these systems. This paper reports
on the implementation of a parallel solver for sparse linear systems of equations
and proposes simple formulas for predicting the speedup in terms of the size of
the linear system and number of processors in the cluster. The iterative solvers
considered in this paper are i – Conjugate Gradient Squared Method (CGS),
ii – Generalised Minimal Residual Method (GMRES) and iii – the Transpose
Free Quasi-Minimal Residual Method (TFQMR) from the Aztec library
implemented with the MPI interface and Parallel Knoppix based cluster.
Keywords: parallel solver, iterative solver, sparse matrix, cluster, MPI, Aztec,
Parallel Knoppix.
1 Introduction
Many computational algorithms in science and engineering give rise to large
sparse linear systems of equations (LSES) which need to be solved as efficiently
as possible. Most modern iterative methods for solving sparse LSES have as
their key computational step the computation
b Ax =(1)
Keywords
parallel solver, iterative solver, sparse matrix, cluster, MPI, Aztec,
Parallel Knoppix.
Related Book
Other papers in this volume
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