This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each sub-iterate is minimized over a certain two-dimensional subspace. Convergence properties of the proposed method are studied in detail. The approach is further developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. The results of numerical experiments are reported to illustrate the performance of exact and inexact variants of the method on several test problems from different application areas.

翻译：本文研究如何加速一类求解线性方程组的两步迭代方法的收敛性。为了实现加速技术，在每次子迭代中，通过将计算近似解对应的残差范数在某个二维子空间上最小化，来优化收敛过程。文中详细分析了所提方法的收敛性质。该方法进一步被推广用于求解由病态问题离散化产生的（正则化）正规方程。通过数值实验，报告了该方法在来自不同应用领域的多个测试问题上的精确与不精确变体的性能表现。