Journal article
Maximum Entropy Elements in the Intersection of an Affine Space and the Cone of Positive Definite Matrices
SIAM journal on matrix analysis and applications, v 16(2), pp 369-376
01 Apr 1995
Abstract
It is shown that for given positive definite $A$ and $B$ and a linear subspace $\mathcal{W}$ consisting of $n \times n$ indefinite (or trivial) Hermitian matrices, there exists a unique positive definite matrix $F$ in $A + \mathcal{W}$ such that $F^{ - 1} - B \in \mathcal{W}^ \bot $. This matrix $F$ appears as the maximizes of a certain entropy function. The theorem generalizes a result on Gaussian measures with prescribed margins. Several special cases are presented, yielding new results and recovering known matrix completion results. In case $\mathcal{W}$ is a coordinate subspace, algorithms to find the optimal $F$ are described and numerical results are presented.
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Details
- Title
- Maximum Entropy Elements in the Intersection of an Affine Space and the Cone of Positive Definite Matrices
- Creators
- Mihaly BakonyiHugo J Woerdeman
- Publication Details
- SIAM journal on matrix analysis and applications, v 16(2), pp 369-376
- Publisher
- Society for Industrial and Applied Mathematics
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1995QP71800003
- Other Identifier
- 991021864942204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied