Can Unconventional Eigenvalue Algorithms Supersede the State of the Art.

SIAM News published in 2000 The best of the 20th Century: Editors Name Top 10 Algorithms including the QR algorithm for computing eigenvalues. We quote: Eigenvalues are arguably the most important numbers associated with matricesand they can be the trickiest to compute. In this proposal the QR algorithm will be revisited. We do not aim at minor improvements, tweaks, or tunings of existing theories and algorithms, but at a fundamental research restart situated at the mathematical foundations underlying this algorithm.

Keywords:Eigenvalues, QR algorithm, Rational driven QR steps, Eigenvalue problems, Aggressive deflation, Adaptive shape selection

Disciplines:Analysis, Applied mathematics in specific fields, General mathematics, History and foundations, Other mathematical sciences and statistics, Computer architecture and networks, Distributed computing, Information sciences, Information systems, Programming languages, Scientific computing, Theoretical computer science, Visual computing, Other information and computing sciences