Linear Algebra Research on the AP1000

This paper gives a report on various results of the Linear Algebra Project on the Fujitsu AP1000 in 1993. These include the general implementation of Distributed BLAS Level 3 subroutines (for the scattered storage scheme). The performance and user interface issues of the implementation will be discussed. Implementations of Distributed BLAS-based LU Decomposition, Cholesky Factorization and Star Product algorithms will be described. The porting of the Basic Fourier Functions, from the Fujitsu-ANU Area-4 Project, on the AP1000 is also discussed. While the parallelization of the main FFT algorithm only involves communication on a single `transposition' step, several optimizations including fast roots of unity calculation, are required for its efficient implementation. Several more optimizations on the Hestenes Singular Value Decomposition algorithm have been investigated, including a BLAS Level 3 like kernel for the main computation and partitioning strategies. A study on how all optimiza..