This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper treats both the theoretical foundations of the subject and the practical computational issues. Topics covered 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; Nystr\"om 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.

翻译：本调查描述了线性代数计算(如乘数矩阵和解决线性系统)的概率算法,侧重于对现实世界问题实例有经证明的跟踪记录的技术,文件既处理主题的理论基础,又处理实际计算问题,所涉专题包括:标准估计;抽样矩阵近似;结构化和非结构化随机嵌入;线性回归问题;低位近似;次空间迭代和Krylov方法;错误估计和适应性;中间和CUR系数化;正-西米地平质矩阵的Nystr\'om近似;单一视图(“流化”)算法;全级递增系数化;线性系统的求解器;以及在机器学习和科学计算中出现的内核矩阵近似。