Design of Systolic arrays for QR Decomposition

In this paper we propose design of three systolic arrays to perform QR decomposition of a square matrix. Our first design is based on Given’s rotation method [1]. In contrast to the earlier designs [1], [2] based on this method, our design uses n(n − 1)/2 homogeneous PEs. Our next design is based on Householder method [4]. This method performs only (n− 1) square root operations in contrast to n(n − 1) square root operations performed in Given’s method [6]. Our third design first reduces the given matrix to Hessenberg form [5] and then applies Q-R decomposition to it.