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math.NA2020★ 2 cited
Rank one tensor completion problem
Mohit Singh, Alexander Shapiro, Rui Zhang
In this paper, we consider the rank-one tensor completion problem. We address the question of existence and uniqueness of the rank-one solution. In particular we show that the glob…
math.ST2020
On characteristic rank for matrix and tensor completion
Alexander Shapiro, Yao Xie, Rui Zhang
In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of…