Maximum determinant positive definite Toeplitz completions

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.

21 pages, in honour of the eightieth birthday of Rien Kaashoek