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：迭代精化（IR）是一种流行的线性方程组求解方法，其核心思想是逐步提高初始近似解的精度。该方法最初旨在提升高斯消元法的求解精度，近年来因其适用于模拟器件和图形处理器等快速低精度硬件而重新引发研究兴趣。当求解方法的误差较小时，IR通常收敛，但已知当误差较大时会出现发散现象。我们提出并分析了一种新颖的IR算法增强方案，通过引入线搜索优化步骤来确保算法不会发散。数值实验验证了我们的理论结果，并展示了所提方案的有效性。