A wavefront algorithm for LU decomposition of a partitioned matrix on VLSI processor
Kenji Onaga, Takahiro Takechi · Journal of Parallel and Distributed Computing · 1986
Abstract This paper presents a design of a wavefront algorithm for computing the LU decomposition of a partitioned k 0 m 0 × k 0 m 0 matrix A on an m 0 × m 0 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 A rr = L rr · U rr ; (2) inversion ( L rr ) −1 , ( U rr ) −1 ; (3) multiplications L pr = A pr · ( U rr ) −1 U rq = ( L rr ) −1 · A rq ; and (4) update A pq ← A pq −1 L pq · U rq where the p, q range is r + 1, … , k 0 and the r range is 1, … , k 0 . 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.