The problem of completing a large low rank matrix using a subset of revealed entries has received much attention in the last ten years. The main result of this paper gives a necessary and sufficient condition, stated in the language of graph limit theory, for a sequence of matrix completion problems with arbitrary missing patterns to be asymptotically solvable. It is then shown that a small modification of the Cand\`es-Recht nuclear norm minimization algorithm provides the required asymptotic solution whenever the sequence of problems is asymptotically solvable. The theory is fully deterministic, with no assumption of randomness. A number of open questions are listed.

翻译：使用一组披露条目完成一大批低级矩阵的问题在过去10年中引起了人们的极大关注。本文件的主要结果以图表限值理论的文字为例,提供了必要和充分的条件,使一组任意缺失模式的矩阵完成问题可以暂时解决,然后表明对Cand ⁇ es-Recht核规范最小化算法稍作修改,在问题序列无症状可溶时,就提供了所需的无症状解决方案。理论是完全决定性的,没有随机性假设。列出了若干开放问题。