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Proceedings Paper

Fast heap transform-based QR-decomposition of real and complex matrices: algorithms and codes
Author(s): Artyom M. Grigoryan
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Paper Abstract

In this paper, we describe a new look on the application of Givens rotations to the QR-decomposition problem, which is similar to the method of Householder transformations. We apply the concept of the discrete heap transform, or signal-induced unitary transforms which had been introduced by Grigoryan (2006) and used in signal and image processing. Both cases of real and complex nonsingular matrices are considered and examples of performing QR-decomposition of square matrices are given. The proposed method of QR-decomposition for the complex matrix is novel and differs from the known method of complex Givens rotation and is based on analytical equations for the heap transforms. Many examples illustrated the proposed heap transform method of QR-decomposition are given, algorithms are described in detail, and MATLAB-based codes are included.

Paper Details

Date Published: 11 March 2015
PDF: 12 pages
Proc. SPIE 9411, Mobile Devices and Multimedia: Enabling Technologies, Algorithms, and Applications 2015, 94110N (11 March 2015); doi: 10.1117/12.2083404
Show Author Affiliations
Artyom M. Grigoryan, The Univ. of Texas at San Antonio (United States)

Published in SPIE Proceedings Vol. 9411:
Mobile Devices and Multimedia: Enabling Technologies, Algorithms, and Applications 2015
Reiner Creutzburg; David Akopian, Editor(s)

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