Sparse matrix calculations on the CRAY-2
This paper presents the results of preliminary testing of sparse matrix routines on a CRAY-2 computer. Initially the main architectural differences between the CRAY-1 and CRAY-2 are briefly outlined. The CRAY- 1 has an asymptotic rate of 150 Mflops on one processor, as against 459 Mflops for the CRAY-2 if both arithmetic pipes are kept busy, and it is shown that this rate is closely approached for large matrix-matrix multiplications. Various linear algebra kernels and corresponding codes have been tested in the sparse matrix case, giving particular emphasis to frontal methods. The frontal matrix is of the form \(\left[\begin{matrix} A\quad B\\ C\quad D\end{matrix} \right],\) where A and D are square matrices of size \(k\) and \(r\), respectively, with \(k\ll r\); and at this stage, \(k\) steps of Gauss elimination are performed on the frontal matrix [the second author, \textit{A. M. Erisman} and \textit{J. K. Reid}, Direct methods for sparse matrices. Oxford: Clarendon Press (1986; Zbl 0604.65011)]. Inner loops are given which lead to good rates. The paper concludes with comments on the use of indirect addressing.
scientific article; zbMATH DE number 4024621