This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is illustrated by its application to several computational problems. This treatment establishes conceptual foundations for randomized numerical linear algebra, and it forges links between algorithms that may initially seem unrelated.

翻译：本短期课程为矩阵计算中的随机算法提供了全新视角，系统探讨了概率方法在数值线性代数算法设计中的差异化应用路径。每个设计模板均通过多个计算问题的实际应用加以阐释，由此构建了随机数值线性代数的概念基础，并建立了看似不相关的各类算法之间的内在联系。