Linear programming and operator means (Q1813693)
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scientific article; zbMATH DE number 4855
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linear programming and operator means |
scientific article; zbMATH DE number 4855 |
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Linear programming and operator means (English)
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25 June 1992
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The author shows that the parallel sum, the shorted operator, the geometric mean, and the cascade limit are all examples of operations that can be described as a solution of suitable linear programming problem in the space of self adjoint operators on a finite-dimensional complex Hilbert space. Absence of duality gap in the corresponding program is proved. This fact implies a new result for the computation of geometric mean of two positive semidefinite matrices.
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parallel sum
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shorted operator
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geometric mean
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cascade limit
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space of self adjoint operators
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finite-dimensional complex Hilbert space
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duality gap
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positive semidefinite matrices
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