Over the past twenty years, dense linear algebra libraries have gone through three generations of public domain general purpose packages. In the seventies, the first generation of packages were EISPACK and LINPACK, which implemented a broad spectrum of algorithms for solving dense linear eigenproblems and dense linear systems. In the late eighties, the second generation package called LAPACK was developed. This package attains high performance in a portable fashion while also improving upon the functionality and robustness of LINPACK and EISPACK. Finally, since the early nineties, a third generation package which ports LAPACK to distributed memory networks of computers has been underway as part of the ScaLAPACK project.PLAPACK is a maturing fourth generation package which uses a more application-centric view of vector and matrix distribution, Physically Based Matrix Distribution. It also uses an "MPI-like" programming interface that hides distribution and indexing details in opaque objects, provides a natural layering in the library, and provides a straight-forward application interface. In this paper, we give an overview of the design of PLAPACK.

In this paper, we present straightforward techniques for a highly efficient, scalable implementation of common matrix–matrix operations generally known as the Level 3 Basic Linear Algebra Subprograms (BLAS). This work builds on our recent discovery of a parallel matrix–matrix multiplication implementation, which has yielded superior performance, and requires little work space. We show that the techniques used for the matrix–matrix multiplication naturally extend to all important Level 3 BLAS and thus this approach becomes an enabling technology for efficient parallel implementation of these routines and libraries that use BLAS. Representative performance results on the Intel Paragon system are given. © 1997 John Wiley & Sons, Ltd.