Maximum determinant positive definite Toeplitz completions

Stefan Sremac; Hugo J. Woerdeman; Henry Wolkowicz

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arXiv · 1802.00653

Maximum determinant positive definite Toeplitz completions

Stefan Sremac·Hugo J. Woerdeman·Henry Wolkowicz

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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.

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Stefan Sremac, Hugo J. Woerdeman, Henry Wolkowicz. 2018-02-02. Maximum determinant positive definite Toeplitz completions. https://arxiv.org/abs/1802.00653

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