Linear Algebra, Computational

Abstract Computational linear algebra is the study of numerical algorithms used to solve linear algebra problems on computers. Consequently, the field can be divided into three parts: discrete computations, constrained optimization, and numerical linear algebra. Due to limitations of space, only the most important topics of numerical linear algebra are discussed. These topics include matrix decompositions, iterative methods for systems of linear equations, updating methods, the underlying principles of numerical stability, accuracy of computed solutions, and high‐quality mathematical software. For each topic, a short overview and best practices are discussed. In selecting or developing methods for solving a problem in computational linear algebra, it is necessary to have an understanding of each of these main features.