An algorithm for finding an optimal projection of a symmetric matrix onto a diagonal matrix (Q2877086)
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scientific article; zbMATH DE number 6333366
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An algorithm for finding an optimal projection of a symmetric matrix onto a diagonal matrix |
scientific article; zbMATH DE number 6333366 |
Statements
21 August 2014
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matrix projection
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matrix embedding
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augmented Lagrangian method
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active-set method
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Stiefel manifold
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Grassmannian manifold
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optimization over Riemannian manifolds
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orthogonality constraints
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algorithm
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numerical test
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An algorithm for finding an optimal projection of a symmetric matrix onto a diagonal matrix (English)
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Motivated by an application in atomic chemistry, the author discusses the problem of finding the optimal projection of a given symmetric matrix onto a given diagonal matrix. Starting with the investigation of two-sided optimization problems, it is shown that they generally do not have unique optimal solutions. Algorithms are proposed to find optimal solutions whose major costs are a few eigenvalue decompositions. Numerical tests are given to test the performance of the new algorithm.
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0.7148564457893372
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0.7125558853149414
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