Results 1 
2 of
2
A PolyAlgorithm for Parallel Dense Matrix Multiplication on TwoDimensional Process Grid Topologies
, 1995
"... In this paper, we present several new and generalized parallel dense matrix multiplication algorithms of the form C = αAB + βC on twodimensional process grid topologies. These algorithms can deal with rectangular matrices distributed on rectangular grids. We classify these algori ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
In this paper, we present several new and generalized parallel dense matrix multiplication algorithms of the form C = &alpha;AB + &beta;C on twodimensional process grid topologies. These algorithms can deal with rectangular matrices distributed on rectangular grids. We classify these algorithms coherently into three categories according to the communication primitives used and thus we offer a taxonomy for this family of related algorithms. All these algorithms are represented in the data distribution independent approach and thus do not require a specific data distribution for correctness. The algorithmic compatibility condition result shown here ensures the correctness of the matrix multiplication. We define and extend the data distribution functions and introduce permutation compatibility and algorithmic compatibility. We also discuss a permutation compatible data distribution (modified virtual 2D data distribution). We conclude that no single algorithm always achieves the best performance...
CRPC Research into Linear Algebra Software for High Performance Computers
, 1994
"... In this paper we look at a number of approaches being investigated in the Center for Research on Parallel Computation (CRPC) to develop linear algebra software for highperformance computers. These approaches are exemplified by the LAPACK, templates, and ARPACK projects. LAPACK is a software library ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
In this paper we look at a number of approaches being investigated in the Center for Research on Parallel Computation (CRPC) to develop linear algebra software for highperformance computers. These approaches are exemplified by the LAPACK, templates, and ARPACK projects. LAPACK is a software library for performing dense and banded linear algebra computations, and was designed to run efficiently on high performance computers. We focus on the design of the distributed memory version of LAPACK, and on an objectoriented interface to LAPACK. The templates project aims at making the task of developing sparse linear algebra software simpler and easier. Reusable software templates are provided that the user can then customize to modify and optimize a particular algorithm, and hence build a more complex applications. ARPACK is a software package for solving large scale eigenvalue problems, and is based on an implicitly restarted variant of the Arnoldi scheme. The paper focuses on issues impact...