论文标题
随机数值线性代数：基础和算法
Randomized Numerical Linear Algebra: Foundations & Algorithms
论文作者
论文摘要
该调查描述了线性代数计算的概率算法，例如分解矩阵和求解线性系统。它着重于具有现实世界中问题实例的可靠记录的技术。该论文既将主题的理论基础和实际计算问题都视为。 涵盖的主题包括规范估计；矩阵近似通过采样；结构化和非结构化随机嵌入；线性回归问题；低级别近似；子空间迭代和Krylov方法；错误估计和适应性；插值和验证；阳性阳性矩阵的Nyström近似；单视图（“流”）算法；全等级的因素化；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的近似。
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; 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.
