2010/06/28 by Rick Ma, Ma, Rick, Samuel Cheng +1 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Block matrix #Combinatorics #Computation #Computer science #Decomposition #Divide and conquer algorithms #Electromagnetic Scattering and Analysis #FOS: Mathematics #LU decomposition #Low-rank approximation #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix completion #Matrix decomposition #Minification #Numerical Analysis (math.NA) #Pure mathematics #Rank (graph theory) #Singular value decomposition #Sparse and Compressive Sensing Techniques #Sparse matrix #Trimming #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1006.5252
published in arXiv (Cornell University) (Cornell University)
arxiv created 2010/06/28 · openalex publication_date 2010/06/28 · arxiv updated 2010/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank completed matrix. The divide-and-conquer approach can significantly reduce computation complexity and storage requirement. Moreover, the proposed decomposition method can be naturally incorporated into any existing matrix completion methods to attain further gain. Unlike most existing approaches, the proposed method is not based on norm minimization nor SVD decomposition. This makes it possible to be applied beyond real domain and can be used in arbitrary fields including finite fields.