Abstract

This paper presents a design of a wavefront algorithm for computing the LU decomposition of a partitioned k0m0 × k0m0 matrix A on an m0 × m0 VLSI array Ω of dataflow type processors with the return path from right to left. The algorithm, based on the block form of Gaussian elimination, consists of four steps: (1) LU decomposition Arr = Lrr · Urr; (2) inversion (Lrr)−1, (Urr)−1; (3) multiplications Lpr = Apr · (Urr)−1Urq = (Lrr)−1 · Arq; and (4) update Apq ← Apq−1Lpq · Urq where the p, q range is r + 1, … , k0 and the r range is 1, … , k0. Each subalgorithm is implemented by distributed programs in the processor array Ω and driven by tokens and synchronized by wavefronts. Each processing element PE of Ω is interconnected through registers of send-if-empty(or idle)-ahead type.

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