Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination, interest in IR has been revived because of its suitability for execution on fast low-precision hardware such as analog devices and graphics processing units. IR generally converges when the error associated with the solution method is small, but is known to diverge when this error is large. We propose and analyze a novel enhancement to the IR algorithm by adding a line search optimization step that guarantees the algorithm will not diverge. Numerical experiments verify our theoretical results and illustrate the effectiveness of our proposed scheme.

翻译：迭代优化（IR）是一种基于逐步改进初始近似解精度的线性方程组求解方案。该算法最初旨在提升高斯消元法的精度，近年来因其适用于模拟设备和图形处理器等快速低精度硬件而重新受到关注。当求解方法相关误差较小时，IR通常收敛；但当误差较大时，已知会出现发散现象。本文通过增加线搜索优化步骤，提出并分析了一种改进的IR算法，该步骤能保证算法不会发散。数值实验验证了理论结果，并证明了所提方案的有效性。