Optimal scheduling algorithms for parallel gaussian elimination

Parallel Gaussian Elimination Using MPI

In this project, we had to implement a parallel solver for linear equation systems, using a technique known as Gaussian elimination (GE). As with many other algorithms for solving linear equation systems, GE is performed on the matrix representation of the system, Ax = b, where A is the coefficient matrix and b is the vector of known values. GE works by applying a set of elementary row operatio...

Communication-Efficient Parallel Gaussian Elimination

Parallel Gaussian Elimination with Linear Work

This paper presents an algorithm for nding parallel elimination orderings for Gaussian elimination. Viewing a system of equations as a graph, the algorithm can be applied directly to interval graphs and chordal graphs. For general graphs, the algorithm can be used to parallelize the ordering produced by some other heuristic such as minimum degree. In this case, the algorithm is applied to the c...

Parallel Gaussian Elimination Using OpenMP and MPI

In this paper, we have presented a parallel algorithm for Gaussian Elimination. Elimination in both a shared memory environment, using OpenMP, and in a distributed memory environment, using MPI. Parallel LU and Gaussian algorithms for linear systems have been studied extensively and the point of this paper is to present the results of examining various load balancing schemes on both platforms. ...

Unified Parallel Algorithms for Gaussian Elimination with Backward Substitution on Product Networks

The increasing interest in product networks (PNs) as a method of combining desirable properties of component networks, has prompted a need for the general study of the algorithmic issues related to this important class of interconnection networks. In this paper we present unified parallel algorithms for Gaussian elimination, with partial and complete pivoting, on product networks. A parallel al...