• Symmetrizing a Hessenberg matrix: Designs for VLSI parallel processor arrays

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/105/01/0059-0071

    • Keywords

       

      Complexity; equivalent symmetric matrix; Hessenberg matrix; symmetrizer; systolic array; VLSI processor array

    • Abstract

       

      A symmetrizer of a nonsymmetric matrix A is the symmetric matrixX that satisfies the equationXA =AtX, wheret indicates the transpose. A symmetrizer is useful in converting a nonsymmetric eigenvalue problem into a symmetric one which is relatively easy to solve and finds applications in stability problems in control theory and in the study of general matrices. Three designs based on VLSI parallel processor arrays are presented to compute a symmetrizer of a lower Hessenberg matrix. Their scope is discussed. The first one is the Leiserson systolic design while the remaining two, viz., the double pipe design and the fitted diagonal design are the derived versions of the first design with improved performance.

    • Author Affiliations

       

      F R K Kumar1 S K Sen1

      1. Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore - 560012, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

© 2017-2019 Indian Academy of Sciences, Bengaluru.