VAPP 1990, CONPAR 1990: CONPAR 90 — VAPP IV pp 131-142

# Parallel givens factorization on a shared memory multiprocessor

• El Mostafa Daoudi
• Gaëtan Libert
Parallel Linear Algebra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 457)

## Abstract

The complexity of parallel Givens factorization on a shared memory architecture composed with p identical processors has been determined for square matrices [6]. For the rectangular case the problem of the optimality (construction and execution time of the optimal algorithm) is still open. In this paper we describe two parallel algorithms to compute the Givens factorization of a rectangular matrix of size mxn (m ≥ n). The first one is formulated for any m, n and p. Its execution time is equal to (mn-n(n+1)/2)/p +3p/2 + o (p). The second one is for p ≤ min(m/4, n/2). Its execution time is equal to (mn-n(n+1)/2)/p + p/2 + o(p) if m-n > p, and (mn-n(n+1)/2)/p + p + (m-n)(m-n-2p)/2p + o(p) if m-n ≤ p. We think that the second algorithm is asymptotically optimal and prove it for m=n.

## Keywords

Parallel linear algebra orthogonal decomposition Givens factorization shared memory multiprocessor complexity of parallel algorithm

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