Optimal ℓ 1 Rank One Matrix Decomposition

Radu Balan (), Kasso A. Okoudjou (), Michael Rawson (), Yang Wang () and Rui Zhang ()
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Radu Balan: University of Maryland
Kasso A. Okoudjou: University of Maryland
Michael Rawson: University of Maryland
Yang Wang: Hong Kong University of Science and Technology
Rui Zhang: Hong Kong University of Science and Technology

A chapter in Harmonic Analysis and Applications, 2021, pp 21-41 from Springer

Abstract: 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.

Keywords: Primary 45P05, 47B10; Secondary 42C15. (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-61887-2_2

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DOI: 10.1007/978-3-030-61887-2_2

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