English

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.

Keywords

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

R2 v1 2026-06-23T00:08:39.185Z