A Look at Scalable Dense Linear Algebra Libraries

J. J. Dongarra

Department of Computer Science

University of Tennessee

Knoxville, TN 37996-1301

U. S. A.

R. A. van de Geijn

Department of Computer Science

The University of Texas at Austin

Austin, TX 78712

U. S. A.

D. W. Walker

Mathematical Sciences Section

Oak Ridge National Laboratory

P. O. Box 2008

Oak Ridge, TN 37831-6367

U. S. A.

Abstract

We discuss the essential design features of a library of scalable software for performing dense linear algebra computations on distributed memory concurrent computers. The square block scattered decomposition is proposed as a flexible and general-purpose way of decomposing most, if not all, dense matrix problems. An object-oriented interface to the library permits more portable applications to be written, and is easy to learn and use, since details of the parallel implementation are hidden from the user. Experiments on the Intel Touchstone Delta system with a prototype code that uses the square block scattered decomposition to perform LU factorization are presented and analyzed. It was found that the code was both scalable and efficient, performing at about 14 Gflop/s (double precision) for the largest problem considered.

J. J. Dongarra, R. A. van de Geijn, and D. W. Walker, A Look at Scalable Dense Linear Algebra Libraries, in Proceedings of the 1992 Scalable High Performance Computing Conference, pages 372-379, ed. J. Saltz, published by IEEE Computer Society Press, 1992.