Factorization of positive-semidefinite operators with absolutely summable entries
| Autor: | Balan, Radu, Jiang, Fushuai |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | A problem by Feichtinger, Heil, and Larson asks whether a positive-definite integral operator with $M_1$ kernel admits a symmetric rank-one decomposition which is strongly square-summable with respect to the $M_1$ norm. In conjunction with a concurrent result by Bandeira-Mixon-Steinerberger, we provide a negative answer to the problem and study special cases where such factorization is possible. We also discuss an application of the results to the semidefinite relaxation of a quadratic program. Comment: 20 pages |
| Databáze: | arXiv |
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