Yet another algorithm for the symmetric eigenvalue problem

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Date
2016-05-10MFO Scientific Program
Research in Pairs 2016Series
Oberwolfach Preprints;2016,02Author
Aurentz, Jared L.
Mach, Thomas
Vandebril, Raf
Watkins, David S.
Metadata
Show full item recordOWP-2016-02
Abstract
In this paper we present a new algorithm for solving the symmetric matrix eigenvalue problem that works by first using a Cayley transformation to convert the symmetric matrix into a unitary one and then uses Gragg’s implicitly shifted unitary QR algorithm to solve the resulting unitary eigenvalue problem. We prove that under reasonable assumptions on the symmetric matrix this algorithm is backward stable and also demonstrate that this algorithm is comparable with other well known implementations in terms of both speed and accuracy.