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

Bini, Dario; Meini, Beatrice; Poloni, Federico

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

An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
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by Dario A. Bini, Beatrice Meini and Federico Poloni PDF

Math. Comp. 79 (2010), 437-452 Request permission

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.

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