Symmetrizing a Hessenberg matrix: Designs for VLSI parallel processor arrays
 F. R. K. Kumar,
 S. K. Sen
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A symmetrizer of a nonsymmetric matrix A is the symmetric matrixX that satisfies the equationXA =A ^{t}X, 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.
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 Title
 Symmetrizing a Hessenberg matrix: Designs for VLSI parallel processor arrays
 Journal

Proceedings of the Indian Academy of Sciences  Mathematical Sciences
Volume 105, Issue 1 , pp 5971
 Cover Date
 19950201
 DOI
 10.1007/BF02840591
 Print ISSN
 03700089
 Online ISSN
 09737685
 Publisher
 Springer India
 Additional Links
 Topics
 Keywords

 Complexity
 equivalent symmetric matrix
 Hessenberg matrix
 symmetrizer
 systolic array
 VLSI processor array
 Industry Sectors
 Authors

 F. R. K. Kumar ^{(1)}
 S. K. Sen ^{(1)}
 Author Affiliations

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