Hardware-Oriented Algorithm for Quaternion-Valued Matrix Decomposition

Abstract

In this brief, a generalized form for 2-, 4-, and 8-D coordinate rotation digital computer (CORDIC) rotation matrices is suggested, and a novel highly parallel efficient hardware-oriented 8-D octonion CORDIC algorithm for quaternion-valued matrix decomposition is designed and presented. Furthermore, a successful sequence of iterations with guaranteed convergence is determined, and the hardware implementation of this algorithm is considered. Such a processor can be utilized to speed up the Givens rotations and computing the QR and singular-value decomposition processes of a quaternion matrix in a digital signal processor.