Maximum determinant positive definite Toeplitz completions

Stefan Sremac; Hugo J. Woerdeman; Henry Wolkowicz

doi:10.1007/978-3-030-04269-1_17

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Maximum determinant positive definite Toeplitz completions

Book chapter

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Maximum determinant positive definite Toeplitz completions

Stefan Sremac, Hugo J. Woerdeman and Henry Wolkowicz

Operator Theory, Analysis and the State Space Approach, pp 421-441

31 Dec 2018

DOI: https://doi.org/10.1007/978-3-030-04269-1_17

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https://arxiv.org/abs/1802.00653View

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Abstract

15A60

15A83

15B05

90C22

Matrix completion

maximum determinant

positive definite completion

singularity degree

Toeplitz matrix

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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Details

Title: Maximum determinant positive definite Toeplitz completions
Creators: Stefan Sremac - University of Waterloo
Hugo J. Woerdeman - Drexel University
Henry Wolkowicz - University of Waterloo
Publication Details: Operator Theory, Analysis and the State Space Approach, pp 421-441
Series: Operator Theory: Advances and Applications
Publisher: Springer International Publishing; Cham
Resource Type: Book chapter
Language: English
Academic Unit: Mathematics
Scopus ID: 2-s2.0-85060135169
Other Identifier: 991019173988404721

Maximum determinant positive definite Toeplitz completions

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Abstract

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