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An effective matrix geometric mean satisfying the Ando-Li-Mathias properties
Author(s):
Dario
A.
Bini;
Beatrice
Meini;
Federico
Poloni.
Journal:
Math. Comp.
79
(2010),
437-452.
MSC (2000):
Primary 65F30;
Secondary 15A48, 47A64
Posted:
June 19, 2009
MathSciNet review:
2552234
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Abstract:
We propose a new matrix geometric mean satisfying the ten properties given by Ando, Li and Mathias [Linear Alg. Appl. 2004]. This mean is the limit of a sequence which converges superlinearly with convergence of order 3 whereas the mean introduced by Ando, Li and Mathias is the limit of a sequence having order of convergence 1. This makes this new mean very easily computable. We provide a geometric interpretation and a generalization which includes as special cases our mean and the Ando-Li-Mathias mean.
References:
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- 1.
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- 2.
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Additional Information:
Dario
A.
Bini
Affiliation:
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
Email:
bini@dm.unipi.it
Beatrice
Meini
Affiliation:
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
Email:
meini@dm.unipi.it
Federico
Poloni
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri 6, 56126 Pisa, Italy
Email:
poloni@sns.it
DOI:
10.1090/S0025-5718-09-02261-3
PII:
S 0025-5718(09)02261-3
Keywords:
Matrix geometric mean,
geometric mean,
positive definite matrix
Received by editor(s):
December 22, 2008
Received by editor(s) in revised form:
January 26, 2009
Posted:
June 19, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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