What is an inductive mean?
Information Theory
2024-10-22 v1 Classical Analysis and ODEs
math.IT
Abstract
An inductive mean is a mean defined as a limit of a convergence sequence of other means. Historically, this notion of inductive means obtained as limits of sequences was pioneered independently by Lagrange and Gauss for defining the arithmetic-geometric mean. In this note, we first explain several generalizations of the scalar geometric mean to symmetric positive-definite matrices, and then present several inductive mean mechanisms for sets of symmetric positive-definite matrices.
Cite
@article{arxiv.2410.15717,
title = {What is an inductive mean?},
author = {Frank Nielsen},
journal= {arXiv preprint arXiv:2410.15717},
year = {2024}
}
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10 pages