A Note On the Rank of the Optimal Matrix in Symmetric Toeplitz Matrix Completion Problem

2019/03/07 by Xihong Yan, Jiahao Guo, Yan, Xihong +3
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1903.02719

openalex publication_date 2019/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the symmetric Toeplitz matrix completion problem, whose matrix under consideration possesses specific row and column structures. This problem, which has wide application in diverse areas, is well-known to be computationally NP-hard. This note provides an upper bound on the objective of minimizing the rank of the symmetric Toeplitz matrix in the completion problem based on the theorems from the trigonometric moment problem and semi-infinite problem. We prove that this upper bound is less than twice the number of linear constraints of the Toeplitz matrix completion problem. Compared with previous work in the literature, ours is one of the first efforts to investigate the bound of the objective value of the Toeplitz matrix completion problem.

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