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Eigenvalue computations are ubiquitous in science and engineering.
John Francis's implicitly shifted QR algorithm has been the method
of choice for small to medium sized eigenvalue problems since its
invention in 1959. This book presents a new view of this classical
algorithm. While Francis's original procedure chases bulges, the
new version chases core transformations, which allows the
development of fast algorithms for eigenvalue problems with a
variety of special structures. This also leads to a fast and
backward stable algorithm for computing the roots of a polynomial
by solving the companion matrix eigenvalue problem. The authors
received a SIAM Outstanding Paper prize for this work. This book
will be of interest to researchers in numerical linear algebra and
their students.
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