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Systolic implementations of up/down-dating cholesky factorization using vectorized Gram-Schmidt pseudo orthoganalization

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Abstract

We propose a new class ofhyperbolic Gram-Schmidt methods to simultaneously update and downdate the Cholesky factor of a sample covariance matrix efficiently with applications to sliding window recursive least squares (RLS) filtering problems. Several vectorized versions of this Gram-Schmidt approach are introduced, which include conventional column-updating, modified row/column-updating, and square-root-free methods. Comparisons to the existing known methods, such as Householder transformation and Givens rotation, are also given. Upon further reformulating these algorithms, a systolic triarray structure is proposed to facilitate VLSI implementations.

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Authors and Affiliations

  1. Department of Communication Engineering, National Chiao Tung University, 30039, Hsinchu, Taiwan

    S. F. Hsieh

  2. Electrical Engineering Department, Systems Research Center, University of Maryland, 20742, College Park, MD

    K. J. R. Liu

  3. Electrical Engineering Department, UCLA, 90024-1594, Los Angeles, CA

    K. Yao

Authors
  1. S. F. Hsieh
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  2. K. J. R. Liu
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  3. K. Yao
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Additional information

This work is partially supported by a UC MICRO grant and the NSF grant NCR-8814407. It is also partially supported by NSF grant ECD-8803012-06.

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Hsieh, S.F., Liu, K.J.R. & Yao, K. Systolic implementations of up/down-dating cholesky factorization using vectorized Gram-Schmidt pseudo orthoganalization. J VLSI Sign Process Syst Sign Image Video Technol 3, 151–161 (1991). https://doi.org/10.1007/BF00925826

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  • DOI: https://doi.org/10.1007/BF00925826

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