English

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}
}

Comments

10 pages

R2 v1 2026-06-28T19:29:14.545Z