Abstract
In this paper, we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of optimality of such decompositions. For some classes of positive semidefinite matrices, we give explicitly these optimal decompositions. These classes include diagonally dominant matrices and certain of their generalizations, 2 × 2, and a class of 3 × 3 matrices.
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Acknowledgements
R. Balan was partially supported by the National Science Foundation grant DMS-1816608 and Laboratory for Telecommunication Sciences under grant H9823031D00560049. K. A. Okoudjou was partially supported by the U S Army Research Office grant W911NF1610008, the National Science Foundation grant DMS 1814253, and an MLK visiting professorship.
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Balan, R., Okoudjou, K.A., Rawson, M., Wang, Y., Zhang, R. (2021). Optimal ℓ 1 Rank One Matrix Decomposition. In: Rassias, M.T. (eds) Harmonic Analysis and Applications. Springer Optimization and Its Applications, vol 168. Springer, Cham. https://doi.org/10.1007/978-3-030-61887-2_2
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DOI: https://doi.org/10.1007/978-3-030-61887-2_2
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