Computing the nearest diagonally dominant matrix (Q2713568)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Computing the nearest diagonally dominant matrix |
scientific article |
Statements
10 June 2001
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diagonally dominant matrices
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matrix cones
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Dykstra's algorithm
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Kuhn-Tucker conditions
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alternating projection algorithm
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numerical experiments
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Computing the nearest diagonally dominant matrix (English)
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The problem of minimizing the distance of a given matrix to the set of symmetric and diagonally dominant matrices with positive diagonal is considered. Using the Kuhn-Tucker condition the authors first characterize the projection onto the cone of diagonally dominant matrices with positive diagonal and then they apply \textit{R. L. Dykstra}'s alternating projection algorithm [J. Am. Stat. Assoc. 78, 837-842 (1983; Zbl 0535.62063)] to force symmetry and, thus, solve the problem. Two different implementations of Dykstra's algorithm applied to the given problem are suggested and and their behaviour on some numerical experiments is discussed.
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