Geodesic
Positive semidefinite solution to matrix completion problem and matrix approximation problem
Filomat, Tome 36 (2022) no. 11, p. 3709

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DOI

In this paper, firstly, we discuss the following matrix completion problem in the spectral norm:∥∥∥∥∥∥ ( A B B∗ X )∥∥∥∥∥∥ 2 1 subject to ( A B B∗ X ) ⩾ 0. The feasible condition for the above problem is established, in this case, the general positive semidefinite solution and its minimum rank are presented. Secondly, applying the result of the above problem, we also study the matrix approximation problem: ∥A − BXB∗∥2 1 subject to A − BXB∗ ⩾ 0, where A ∈ Cm×m⩾ , B ∈ Cm×n, and X ∈ Cn×n⩾ .
DOI : 10.2298/FIL2211709L
Classification : 15A24, 15A60, 93A10
Keywords: Matrix approximation problem, Matrix completion problem, Positive semidefinite solution, Spectral norm 
Xifu Liu. Positive semidefinite solution to matrix completion problem and matrix approximation problem. Filomat, Tome 36 (2022) no. 11, p. 3709 . doi: 10.2298/FIL2211709L
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     author = {Xifu Liu},
     title = {Positive semidefinite solution to matrix completion problem and matrix approximation problem},
     journal = {Filomat},
     pages = {3709 },
     year = {2022},
     volume = {36},
     number = {11},
     doi = {10.2298/FIL2211709L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2211709L/}
}
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