Maximum determinant positive definite Toeplitz completions
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.
KeywordsMatrix completion Toeplitz matrix positive definite completion maximum determinant singularity degree
Mathematics Subject Classification (2010)15A60 15A83 15B05 90C22
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