IAM 02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
New deterministic approaches to the least square mean
Autor/es:
GHIGLIONI, EDUARDO M.
Revista:
LINEAR ALGEBRA AND ITS APPLICATIONS
Editorial:
ELSEVIER SCIENCE INC
Referencias:
Año: 2020 vol. 585 p. 50 - 59
ISSN:
0024-3795
Resumen:
In this paper we present new deterministic approximations to the least square mean, also called geometric mean or barycenter of a finite collection of positive definite matrices. Let A1,A2,?,Am be any elements of Md(C)+, where the set Md(C)+ is the open cone in the real vector space of selfadjoint matrices H(n). We consider a sequence of blocks of m matrices, that is, (A1,?,Am,A1,?,Am,A1,?Am,?). We take a permutation on every block and then take the usual inductive mean of that new sequence. The main result of this work is that the inductive mean of this block permutation sequence approximate the least square mean on Md(C)+. This generalizes a Theorem obtain by Holbrook. Even more, we have an estimate for the rate of convergence.
