An effective matrix geometric mean satisfying the ando-li-mathias properties

Mathematics of Computation

Volumn 79, Issue 269, 2010, Pages 437-452

  Bini, Dario A ^a   Meini, Beatrice ^a   Poloni, Federico ^b  

^a UNIVERSITY OF PISA   (Italy)

^b SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

Geometric mean; Matrix geometric mean; Positive definite matrix

Indexed keywords

EID: 77952792929     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-09-02261-3     Document Type: Article

References (9)

1. T. Ando, Chi-Kwong Li, and Roy Mathias, Geometric means, Linear Algebra Appl. 385 (2004), 305-334.
2. Rajendra Bhatia, Positive definite matrices, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, 2007
3. Rajendra Bhatia and John Holbrook, Noncommutative geometric means, Math. Intelligencer 28 (2006), no. 1, 32-39.
4. Rajendra Bhatia.; Riemannian geometry and matrix geometric means, Linear Algebra Appl. 413 (2006), no. 2-3, 594-618.
5. R. F. S. Hearmon, The elastic constants of piezoelectric crystals,J.Appl.Phys.3 (1952), 120-123.
6. Nicholas J. Higham, The Matrix Computation Toolbox, http://www.ma.man.ac.uk/~higham/mctoolbox.
7. Bruno Iannazzo and Beatrice Meini, Palindromic matrix polynomials and their relationships with certain functions of matrices, Tech. Report, Dipartimento di Matematica, Universitàdi Pisa, 2009.
8. Yongdo Lim, On Ando-Li-Mathias geometric mean equations, Linear Algebra Appl. 428 (2008), no. 8-9, 1767-1777.
9. Maher Moakher, On the averaging of symmetric positive-definite tensors, J. Elasticity 82 (2006), no. 3, 273-296.