This survey provides an introduction to the use of randomization in the design of fast algorithms for numerical linear algebra. These algorithms typically examine only a subset of the input to solve basic problems approximately, including matrix multiplication, regression and low-rank approximation. The survey describes the key ideas and gives complete proofs of the main results in the field. A central unifying idea is sampling the columns (or rows) of a matrix according to their squared lengths.

中文翻译：

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数值线性代数中的随机算法

本综述介绍了在数值线性代数的快速算法设计中使用随机化。这些算法通常只检查输入的一个子集来近似解决基本问题，包括矩阵乘法、回归和低秩逼近。该调查描述了关键思想并对该领域的主要结果提供了完整的证明。一个中心统一的想法是根据矩阵的平方长度对矩阵的列（或行）进行采样。