Carlson's iterative mean algorithm of positive definite matrices

Title
Carlson's iterative mean algorithm of positive definite matrices
Author(s)
이호수Lim, Yongdo[Lim, Yongdo]
Keywords
GEOMETRIC MEANS; OPERATORS; METRICS
Issue Date
201308
Publisher
ELSEVIER SCIENCE INC
Citation
LINEAR ALGEBRA AND ITS APPLICATIONS, v.439, no.4, pp.1183 - 1201
Abstract
In this paper we propose an iterative mean algorithm involving arithmetic and geometric means of n positive definite matrices which generalizes the 3-dimensional algorithm of positive reals discovered by Carlson (1970) [10]. We show that the iterative mean algorithm is convergent and the common limit satisfies multidimensional versions of all properties (permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities) that one would expect for the Carlson mean of positive reals. Convergence and perturbation analysis with numerical experiments are presented in terms of the Thompson metric and the spectral norm. (C) 2013 Elsevier Inc. All rights reserved.
URI
http://hdl.handle.net/YU.REPOSITORY/29212http://dx.doi.org/10.1016/j.laa.2013.04.005
ISSN
0024-3795
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기초교육대학 > 교양학부 > Articles
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