This paper aims to survey fast methods of verifying the accuracy of a numerical solution of a linear systems. For the last decade, a number of fast verification algorithms have been proposed to obtain an error bound of a numerical solution of a dense or sparse linear system. Such fast algorithms rely on the verified numerical computation using floating-point arithmetic defined by IEEE standard 754. Some fast verification methods for dense and sparse linear systems are reviewed together with corresponding numerical results to show the practical use and efficiency of the verified numerical computation as much as possible.

中文翻译：

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线性系统的快速验证解决方案

本文旨在研究验证线性系统数值解精度的快速方法。在过去的十年中，已经提出了许多快速验证算法来获得稠密或稀疏线性系统的数值解的误差界。这种快速算法依赖于使用 IEEE 标准 754 定义的浮点算术验证的数值计算。回顾了稠密和稀疏线性系统的一些快速验证方法以及相应的数值结果，以显示验证数值计算的实际用途和效率，如尽可能。