Title: Geometric means of structured matrices
Authors: Bini, Dario A. ×
Iannazzo, Bruno
Jeuris, Ben
Vandebril, Raf #
Issue Date: Mar-2014
Publisher: BIT Foundation
Series Title: BIT vol:54 issue:1 pages:55-83
Article number: DOI 10.1007/s10543-013-0450-4
Abstract: The geometric mean of positive definite matrices is usually identified
with the Karcher mean, which possesses all properties—generalized from the
scalar case— a geometric mean is expected to satisfy. Unfortunately,
the Karcher mean is typically not structure preserving, and destroys,
e.g., Toeplitz and band structures, which emerge in many
applications. For this reason, the Karcher mean is not always
recommended for modeling averages of structured matrices. In this
article a new definition of a geometric mean for structured matrices
is introduced, its properties are outlined, algorithms for its
computation, and numerical experiments are provided. In the Toeplitz case an existing mean based on the Kahler metric is analyzed for comparison.
ISSN: 0006-3835
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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