Title: A comparison between the eigenvalue solvers based on semiseparable and tridiagonal matrices
Authors: Vandebril, Raf
Van Barel, Marc
Mastronardi, Nicola #
Issue Date: 2004
Conference: V International Workshop on Accurate Solution of Eigenvalue Problems location:Arcadeon Conference Center; Hagen, Germany date:June 28 - July 1, 2004
Abstract: In this poster we will investigate an algorithm which computes the
eigenvalues of symmetric matrices via semiseparable matrices,
w.r.t. to accuracy and deflation possibilities.

A brief introduction will be given to explore the method to
compute eigenvalues via semiseparable matrices instead of via (their
inverses) the tridiagonal
matrices. A similarity reduction of a symmetric matrix to a similar
semiseparable one is introduced followed by an implicit QR-method
for these symmetric semiseparable matrices.

The main goal of this talk is to compare both algorithms as they are
similar to each other. A first important thing to consider is the
complexity of both of the algorithms. One step of the QR-method applied
to semiseparable matrices costs more than the corresponding
QR-step applied to tridiagonal matrices. But, the semiseparable
approach needs less iterations to converge to an eigenvalue.
A comparison of the complexity of both of the algorithms will be made. Moreover, we will prove that
the semiseparable approach, has an additional advantage with respect to
the tridiagonal approach. The reduction to semiseparable form
performs also some kind of subspace iteration. This behavior will
increase the deflation possibilities of the semiseparable approach
w.r.t. the traditional approach, in case there are different clusters
of eigenvalues.
Publication status: published
KU Leuven publication type: IMa
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
Electrical Engineering - miscellaneous
# (joint) last author

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