A systolic rank revealing QR algorithm

Abstract

In many fields of signal and image processing control, and telecommunication there is much interest today in the numerical techniques offered by linear algebra. The singular value decomposition (SVD) is one of the techniques which have proven useful in many engineering applications, but unfortunately its computation is a costly procedure. The QR factorization (QRF) requires much less computational effort, but rank and null-space estimates are not necessarily reliable. This paper presents a version of rank revealing QR (RRQR) algorithm which is suited for implementation on a VLSI systolic array. The implementation of the RRQRF requires n(n+1)/2 processors and O(n) external buffers, for a problem of order n. The execution time for the algorithm is O(nr), where r is A's numerical rank.<>