Hardware-Oriented Algorithm for Quaternion-Valued Matrix Decomposition

Author

Doukhnitch, Evgueni ; Ozen, Emre

Author_Institution

Dept. of Comput. Eng., Istanbul Aydyn Univ., Istanbul, Turkey

Volume

58

Issue

4

fYear

2011

fDate

4/1/2011 12:00:00 AM

Firstpage

225

Lastpage

229

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.

Keywords

digital signal processing chips; iterative methods; singular value decomposition; 2D coordinate rotation digital computer rotation matrix; 4D coordinate rotation digital computer rotation matrix; 8D coordinate rotation digital computer rotation matrix; 8D octonion CORDIC algorithm; Givens rotation; QR computation; digital signal processor; hardware-oriented algorithm; quaternion-valued matrix decomposition; singular-value decomposition process; Algorithm design and analysis; Convergence; Jacobian matrices; Matrix decomposition; Parallel processing; Quaternions; Signal processing algorithms; Givens rotations; QR decomposition and singular-value decomposition (SVD); processor arrays; quaternion matrix;

fLanguage

English

Journal_Title

Circuits and Systems II: Express Briefs, IEEE Transactions on

Publisher

ieee

ISSN

1549-7747

Type

jour

DOI

10.1109/TCSII.2011.2111590

Filename

5720288