What is an inductive mean?
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912079403810816 |
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| author | Nielsen, Frank |
| author_facet | Nielsen, Frank |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | What is an inductive mean? Nielsen, Frank Information Theory Classical Analysis and ODEs 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. |
| title | What is an inductive mean? |
| topic | Information Theory Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2410.15717 |