Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of them.1This informal yet practical definition captures the essence of the goal of direct methods for solving sparse matrix problems. They exploit the sparsity of a matrix to solve problems economically: much faster and using far less memory than if all the entries of a matrix were stored and took part in explicit computations. These methods form the backbone of a wide range of problems in computational science. A glimpse of the breadth of applications relying on sparse solvers can be seen in the origins of matrices in published matrix benchmark collections (Duff and Reid 1979a, Duff, Grimes and Lewis 1989a, Davis and Hu 2011). The goal of this survey article is to impart a working knowledge of the underlying theory and practice of sparse direct methods for solving linear systems and least-squares problems, and to provide an overview of the algorithms, data structures, and software available to solve these problems, so that the reader can both understand the methods and know how best to use them.

中文翻译：

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稀疏线性系统的直接方法综述

Wilkinson 将稀疏矩阵定义为一个具有足够多的零以利用它们的矩阵。1这个非正式但实用的定义抓住了解决稀疏矩阵问题的直接方法目标的本质。他们利用矩阵的稀疏性来经济地解决问题：与存储矩阵的所有条目并参与显式计算相比，速度要快得多，并且使用的内存要少得多。这些方法构成了计算科学中广泛问题的支柱。可以在已发布的矩阵基准集合中的矩阵起源中看到依赖稀疏求解器的应用程序的广度（Duff 和 Reid 1979一种, 达夫、格莱姆斯和刘易斯 1989一种, 戴维斯和胡 2011)。这篇综述文章的目的是传授有关解决线性系统和最小二乘问题的稀疏直接方法的基本理论和实践的工作知识，并概述可用于解决这些问题的算法、数据结构和软件问题，以便读者既能理解方法，又能知道如何最好地使用它们。