Symmetrizing a Hessenberg matrix: Designs for VLSI parallel processor arrays |
| |
Authors: | F R K Kumar S K Sen |
| |
Institution: | (1) Supercomputer Education and Research Centre, Indian Institute of Science, 560012 Bangalore, India |
| |
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 |
本文献已被 SpringerLink 等数据库收录! |