Completion of Hankel partial contractions of extremal type
- 1 December 2012
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 53 (12), 123526
- https://doi.org/10.1063/1.4769992
Abstract
We find concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size 4 × 4 in the extremal case. Along the way we introduce a new approach that allows us to solve, algorithmically, the contractive completion problem for 4 × 4 Hankel matrices. As an application, we obtain a concrete example of a partially contractive 4 × 4 Hankel matrix, which does not admit a contractive completion.Funding Information
- National Science Foundation (DMS-0400741, DMS-0801168)
This publication has 13 references indexed in Scilit:
- On completion problems for various classes of P-matricesLinear Algebra and its Applications, 2005
- Matrix completion problems for pairs of related classes of matricesLinear Algebra and its Applications, 2003
- A connection between positive semidefinite and euclidean distance matrix completion problemsLinear Algebra and its Applications, 1998
- Contractive Completions of Hankel Partial ContractionsJournal of Mathematical Analysis and Applications, 1996
- Completion of Toeplitz Partial ContractionsSIAM Journal on Matrix Analysis and Applications, 1988
- Completion of partial matrices to contractionsJournal of Functional Analysis, 1986
- Norm-Preserving Dilations and Their Applications to Optimal Error BoundsSIAM Journal on Numerical Analysis, 1982
- An extremal problem for extensions of a sesquillinear formLinear Algebra and its Applications, 1976
- Interpolation problems in nest algebrasJournal of Functional Analysis, 1975
- On unbounded toeplitz matrices and nonstationary time series with an application to information theoryInformation and Control, 1974