A hexagonally connected processor array for Jacobi-type matrix algorithms∗

Indexing terms : Parallel algorithms, systolic arrays, matrix computation Jacobi-type matrix algorithms are mostly implemented on orthogonally connected processor arrays. In this letter, an alternative partitioning is described, resulting in a grid of hexagonally connected processors. This partitioning is shown to be over four times more efficient, as compared to the original configuration. Introduction Linear algebra and matrix computation play a central role in modern digital signal processing. Representative areas in which matrix computation is important include beamforming, direction finding, spectrum analysis, image processing, etc. For applications with substantial computational requirements, e.g. when a real time implementation is aimed at, parallel algorithms and architectures are indispensable. Systolic or wavefront arrays then provide a means of exploiting large amounts of parallelism and hence achieving orders of magnitude improvement in performance, consistent with the requirements1. Practical parallel algorithms for most of the key matrix operations are by now available. As for the matrix decomposition problems, most often methods are selected that are based on locally computed plane transformations. All of these are inspired by Jacobi’s algorithm for the symmetric eigenvalue decomposition (SEVD). Parallel Jacobitype algorithms are available for the Schur decomposition2, the singular value decomposition (SVD)3, generalized SVD’s, the QR decomposition, etc. In the next section, we first briefly review the conventional systolic implementation for Jacobi-type algorithms. The processor utilization is seen to be particularly low, as each processor is active only one fourth of the time. Next, we show how a different partitioning results in a completely different array, which is over four times more efficient. Systolic arrays for Jacobi-type algorithms ∗This work was sponsored (partly) by the BRA 3280 project of the EC.