Maximum determinant positive definite Toeplitz completions
Optimization and Control
2018-02-05 v1
Abstract
We consider partial symmetric Toeplitz matrices where a positive definite completion exists. We characterize those patterns where the maximum determinant completion is itself Toeplitz. We then extend these results with positive definite replaced by positive semidefinite, and maximum determinant replaced by maximum rank. These results are used to determine the singularity degree of a family of semidefinite optimization problems.
Cite
@article{arxiv.1802.00653,
title = {Maximum determinant positive definite Toeplitz completions},
author = {Stefan Sremac and Hugo J. Woerdeman and Henry Wolkowicz},
journal= {arXiv preprint arXiv:1802.00653},
year = {2018}
}
Comments
21 pages, in honour of the eightieth birthday of Rien Kaashoek