A local inverse formula and a factorization
- Publication Type:
- Chapter
- Citation:
- Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp. 1109 - 1126
- Issue Date:
- 2018-05-23
Closed Access
Filename | Description | Size | |||
---|---|---|---|---|---|
Pages from 2018_Book_ContemporaryComputationalMathe(1).pdf | Published version | 237.85 kB |
Copyright Clearance Process
- Recently Added
- In Progress
- Closed Access
This item is closed access and not available.
© Springer International Publishing AG, part of Springer Nature 2018. All rights reserved. When a matrix has a banded inverse there is a remarkable formula that quickly computes that inverse, using only local information in the original matrix. This local inverse formula holds more generally, for matrices with sparsity patterns that are examples of chordal graphs or perfect eliminators. The formula has a long history going back at least as far as the completion problem for covariance matrices with missing data. Maximum entropy estimates, log-determinants, rank conditions, the Nullity Theorem and wavelets are all closely related, and the formula has found wide applications in machine learning and graphical models.We describe that local inverse and explain how it can be understood as a matrix factorization.
Please use this identifier to cite or link to this item: