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SVD-updating using orthonormal μ-rotations

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Abstract

In this paper the implementation of the SVD-updating algorithm using orthonormal μ-rotations is presented. An orthonormal μ-rotation is a rotation by an angle of a given set of μ-rotation angles (e.g., the angles Φi = arctan2-i) which are choosen such that the rotation can be implemented by a small amount of shift-add operations. A version of the SVD-updating algorithm is used where all computations are entirely based on the evaluation and application of orthonormal rotations. Therefore, in this form the SVD-updating algorithm is amenable to an implementation using orthonormal μ-rotations, i.e., each rotation executed in the SVD-updating algorithm will be approximated by orthonormal μ-rotations. For all the approximations the same accuracy is used, i.e., onlyr≪w (w: wordlength) orthonormal μ-rotations are used to approximate the exact rotation. The rotation evaluation can also be performed by the execution of μ-rotations such that the complete SVD-updating algorithm can be expressed in terms of orthonormal μ-rotations. Simulations show the efficiency of the SVD-updating algorithm based on orthonormal μ-rotations.

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Authors and Affiliations

  1. Institute of Network Theory and Circuit Design, Technical University of Munich, D-80290, Munich, Germany

    Jürgen Götze & Peter Rieder

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  1. Jürgen Götze
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  2. Peter Rieder
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This work was done while with Rice University, Houston, Texas supported by the Alexander von Humbodt Foundation and Texas Advanced Technology Program.

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Götze, J., Rieder, P. SVD-updating using orthonormal μ-rotations. J VLSI Sign Process Syst Sign Image Video Technol 14, 7–17 (1996). https://doi.org/10.1007/BF00925264

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  • DOI: https://doi.org/10.1007/BF00925264

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