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Maximum determinant positive definite Toeplitz completions

  • Stefan Sremac
  • Hugo J. Woerdeman
  • Henry Wolkowicz
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 271)

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

Matrix completion Toeplitz matrix positive definite completion maximum determinant singularity degree 

Mathematics Subject Classification (2010)

15A60 15A83 15B05 90C22 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Stefan Sremac
    • 1
  • Hugo J. Woerdeman
    • 2
  • Henry Wolkowicz
    • 1
  1. 1.Department of Combinatorics and Optimization, Faculty of MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of MathematicsDrexel UniversityPhiladelphiaUSA

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