The CORDIC Householder algorithm

Abstract

A novel n-dimensional (n-D) CORDIC algorithm for Euclidean and pseudo-Euclidean rotations is proposed. This algorithm is closely related to Householder transformations. It is shown to converge faster than CORDIC algorithms developed earlier for n=3 and 4. Processor architectures for the algorithm are presented. The area and time performance of n-D CORDIC processors are evaluated. For a comparable time performance, the processors require significantly less area than parallel Householder processors. Furthermore, arrays of n-D Euclidean CORDIC processors are shown to speed up the QR decomposition of rectangular matrices by a factor of n-1 in comparison with a 2-D CORDIC processor array.<>