Abstract
The QR algorithm is one of the most widely used algorithms for calculating the eigenvalues of matrices. The multishift QR algorithm with multiplicity m is a version that effects m iterations of the QR algorithm at a time. It is known that roundoff errors cause the multishift QR algorithm to perform poorly when m is large. In this paper the mechanism by which the shifts are transmitted through the matrix in the course of a multishift QR iteration is identified. Numerical evidence showing that the mechanism works well when m is small and poorly when m is large is presented. When the mechanism works poorly, the convergence of the algorithm is degraded proportionately.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
