Pipeline givens sequences for computing the qr decomposition on a erew pram

Abstract

Parallel Givens sequences for computing the QR decomposition of an m × n (m > n) matrix are considered. The Givens rotations operate on adjacent planes. A pipeline strategy for updating the pair of elements in the affected rows of the matrix is employed. This allows a Givens rotation to use rows that have been partially updated by previous rotations. Two new Givens schemes, based on this pipeline approach, and requiring respectively n 2/2 and n processors, are developed. Within this context a performance analysis on an exclusive-read, exclusive-write (EREW) parallel random access machine (PRAM) computational model establishes that the proposed schemes are twice as efficient as existing Givens sequences.