An implicit multishift QR-algorithm for symmetric plus low rank matrices

  • VANDEBRIL R
  • DEL CORSO, GIANNA MARIA
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Publication date
January 2010

Abstract

Hermitian plus possibly non-Hermitian low rank matrices can be efficiently reduced into Hessenberg form. The resulting Hessenberg matrix can still be written as the sum of a Hermitian plus low rank matrix. In this paper we develop a new implicit multishift QR-algorithm for Hessenberg matrices, which are the sum of a Hermitian plus a possibly non-Hermitian low rank correction. The proposed algorithm exploits both the symmetry and low rank structure to obtain a QR-step involving only O(n) floating point operations instead of the standard O(n(2)) operations needed for performing a QR-step on a Hessenberg matrix. The algorithm is based on a suitable O(n) representation of the Hessenberg matrix. The low rank parts present in both the Hermitian a...

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