This survey describes probabilistic algorithms for linear algebraic computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problems. The paper treats both the theoretical foundations of the subject and practical computational issues.Topics include norm estimation, matrix approximation by sampling, structured and unstructured random embeddings, linear regression problems, low-rank approximation, subspace iteration and Krylov methods, error estimation and adaptivity, interpolatory and CUR factorizations, Nyström approximation of positive semidefinite matrices, single-view (‘streaming’) algorithms, full rank-revealing factorizations, solvers for linear systems, and approximation of kernel matrices that arise in machine learning and in scientific computing.

中文翻译：

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随机数值线性代数：基础和算法

本综述描述了用于线性代数计算的概率算法，例如分解矩阵和求解线性系统。它侧重于对现实世界问题具有良好记录的技术。本文处理了该主题的理论基础和实际计算问题。主题包括范数估计、采样矩阵逼近、结构化和非结构化随机嵌入、线性回归问题、低秩逼近、子空间迭代和 Krylov 方法、误差估计和自适应性、插值和 CUR 因式分解、正半定矩阵的 Nyström 逼近、单视图（“流式”）算法、全秩揭示因式分解、线性系统的求解器以及机器学习和科学计算中出现的核矩阵逼近。