An effective matrix geometric mean satisfying the Ando-Li-Mathias properties


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.

DOI: 10.1090/S0025-5718-09-02261-3

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Piazza dei Cavalieri 6, 56126 Pisa, Italy E-mail address: poloni@sns

  • Normale Scuola, Superiore

Pontecorvo 5, 56127 Pisa, Italy E-mail address: meini@dm.unipi

  • Dipartimento Di Matematica, Università Di Pisa, B Largo

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