1 |
H.H. Bauschke, S.M. Moffat, X. Wang, The resolvent average for positive semidefinite matrices, Linear Algebra Appl. 432 (2010), 1757-1771.
DOI
|
2 |
Y. Lim and M. P´alfia, Matrix power mean and the Karcher mean, J. Functional Analysis 262 (2012), 1498-1514.
DOI
|
3 |
J. Lawson and Y. Lim, Monotonic properties of the least squares mean, Math. Ann. 351 (2011), 267-279.
DOI
|
4 |
J. Lawson and Y. Lim, Karcher means and Karcher equations of positive definite operators, Trans. Amer. Math. Soc. Series B 1 (2014), 1-22.
DOI
|
5 |
J. Lawson, H. Lee and Y. Lim, Weighted geometric means, Forum Math. 24 (2012), 1067-1090.
DOI
|
6 |
Y. Lim and M. P´alfia, Weighted deterministic walks and no dice approach for the least squares mean on Hadamard spaces, Bull. London Math. Soc. 46 (2014), 561-570.
DOI
|
7 |
M. Sagae and K. Tanabe, Upper and lower bounds for the arithmetic-geometric-harmonic means of positive definite matrices, Linear and Multilinear Algebra 37 (1994), 279-282.
DOI
|
8 |
K.-T. Sturm, Probability measures on metric spaces of nonpositive curvature, in: Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces? Eds. P. Auscher et. al., Contemp. Math. 338, Amer. Math. Soc. (AMS), Providence, 2003.
|
9 |
T. Ando, C.-K. Li, and R. Mathias, Geometric means, Linear Algebra Appl. 385 (2004), 305-334.
DOI
|
10 |
R. Bhatia, Positive Definite Matrices, Princeton Series in Applied Mathematics, 2007.
|
11 |
J. Holbrook, No dice: a determinic approach to the Cartan centroid, J. Ramanujan Math. Soc. 27 (2012), 509-521.
|
12 |
H. Karcher, Riemannian center of mass and mollifier smoothing, Comm. Pure Appl. Math. 30 (1977), 509–541.
DOI
|
13 |
S. Kim, U. Ji, and S. Kum, An approach to the Log-Euclidean mean via the Karcher mean on symmetric cones, Taiwanese J. Math., to be published.
|
14 |
S. Kim, J. Lawson, and Y. Lim, The matrix geometric mean of parameterized, weighted arithmetic and harmonic means, Linear Algebra Appl. 435 (2011), 2114-2131.
DOI
|
15 |
S. Kim and D. Petz, A new proof to construct multivariable geometric means by symmetrization, J. Appl. Math. & Informatics 33 (2015), 379-386.
DOI
|
16 |
F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246 (1979/80), 205-224.
DOI
|
17 |
S. Kum and Y. Lim, Nonexpansiveness of the resolvent average, J. Math. Anal. Appl. 432 (2015), 918-927.
DOI
|