Article

Proceedings of the Indian Academy of Sciences - Mathematical Sciences

, Volume 105, Issue 1, pp 59-71

Symmetrizing a Hessenberg matrix: Designs for VLSI parallel processor arrays

  • F. R. K. KumarAffiliated withSupercomputer Education and Research Centre, Indian Institute of Science
  • , S. K. SenAffiliated withSupercomputer Education and Research Centre, Indian Institute of Science

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Abstract

A symmetrizer of a nonsymmetric matrix A is the symmetric matrixX that satisfies the equationXA =A tX, 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.

Keywords

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