The Matrix Means Toolbox includes the following files:|
alm.m - Computes the Ando-Li-Mathias mean of k matrices 
cheap.m - Computes the cheap mean of k matrices 
dist.m - Computes the Riemannian and Euclidean distance between A and B
explog.m - Computes the explog mean of k matrices 
geomean.m - Computes the geometric mean of two matrice with three algorithms 
gradient.m - Computes the Karcher mean of k matrices using the Riemannian gradient descent 
nbmp.m - Computes the Nakamura/Bini-Meini-Poloni mean of k matrices [5,8]
random.m - Generates k random positive definite matrices
rich.m - Computes the Karcher mean of k matrices using a Richardson-like iteration 
sharp.m - Computes $A\#_t B$
 T. Ando, C.-K. Li and R. Mathias, Geometric means, Linear Algebra Appl., 385-1 (2004) pp. 305-334.
 V. Arsigny, P. Fillard, X. Pennec and N. Ayache, Geometric means in a novel vector space structure on symmetric positive-definite matrices, SIAM J. Matrix Anal. Appl., 29-1 (2006/07), pp. 328-347.
 D. A. Bini and B. Iannazzo, A note on computing matrix geometric means, to
appear in Advances Comp. Math., 35-2/4 (2010), pp. 175-192.
 D. A. Bini and B. Iannazzo, Computing the Karcher mean of symmetric positive definite matrices, to appear in Linear Algebra Appl., 2012.
 D. A. Bini, B. Meini and F. Poloni, An effective matrix geometric mean satisfying the Ando-Li-Mathias properties, Math. Comp., 79 (2010), pp. 437-452.
 B. Iannazzo and B. Meini, The Palyndromic Cyclic Reduction and the Matrix Geometric Mean, Manuscript.
 J. H. Manton, A globally convergent numerical algorithm for computing the centre of mass on compact lie groups, Eighth International Conference on Contro, Automation, Robotics and Vision, 2004. ICARCV 2004 8th, Kunming, China.
 K. Nakamura, Geometric Means of Positive Operators, Kyungpook Math. J. 49 (2009), 167-181
mmtoolbox 1.1b2 - November 26, 2011 - Some minor adjustments to the formatting
of the files.
mmtoolbox 1.1b1 - August, 19, 2011 - rewritten all files from scratch with a uniform style, help in line,
and more; changed the square root computation to the Cholesky factor whenever possible;
changed the name of the file manton.m to gradient.m; changed the name of the file bmp.m to nbmp.m, as
soon as the reference  was individuated; fixed a bug in dist.m.
mmtoolbox 1.0 - July 11, 2010 - first release