  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.
