JOURNAL BROWSE
Search
Advanced SearchSearch Tips
REMARKS ON CONVERGENCE OF INDUCTIVE MEANS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
REMARKS ON CONVERGENCE OF INDUCTIVE MEANS
PARK, JISU; KIM, SEJONG;
 
 Abstract
We define new inductive mean constructed by a mean on a complete metric space, and see its convergence when the intrinsic mean is given. We also give many examples of inductive matrix means and claim that the limit of inductive mean constructed by the intrinsic mean is not the Karcher mean, in general.
 Keywords
Intrinsic mean;inductive mean;Karcher mean;
 Language
English
 Cited by
 References
1.
T. Ando, C.-K. Li, and R. Mathias, Geometric means, Linear Algebra Appl. 385 (2004), 305-334. crossref(new window)

2.
H.H. Bauschke, S.M. Moffat, X. Wang, The resolvent average for positive semidefinite matrices, Linear Algebra Appl. 432 (2010), 1757-1771. crossref(new window)

3.
R. Bhatia, Positive Definite Matrices, Princeton Series in Applied Mathematics, 2007.

4.
J. Holbrook, No dice: a determinic approach to the Cartan centroid, J. Ramanujan Math. Soc. 27 (2012), 509-521.

5.
H. Karcher, Riemannian center of mass and mollifier smoothing, Comm. Pure Appl. Math. 30 (1977), 509–541. crossref(new window)

6.
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.

7.
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. crossref(new window)

8.
S. Kim and D. Petz, A new proof to construct multivariable geometric means by symmetrization, J. Appl. Math. & Informatics 33 (2015), 379-386. crossref(new window)

9.
F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246 (1979/80), 205-224. crossref(new window)

10.
S. Kum and Y. Lim, Nonexpansiveness of the resolvent average, J. Math. Anal. Appl. 432 (2015), 918-927. crossref(new window)

11.
J. Lawson and Y. Lim, Monotonic properties of the least squares mean, Math. Ann. 351 (2011), 267-279. crossref(new window)

12.
J. Lawson and Y. Lim, Karcher means and Karcher equations of positive definite operators, Trans. Amer. Math. Soc. Series B 1 (2014), 1-22. crossref(new window)

13.
J. Lawson, H. Lee and Y. Lim, Weighted geometric means, Forum Math. 24 (2012), 1067-1090. crossref(new window)

14.
Y. Lim and M. P´alfia, Matrix power mean and the Karcher mean, J. Functional Analysis 262 (2012), 1498-1514. crossref(new window)

15.
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. crossref(new window)

16.
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. crossref(new window)

17.
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.