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：本文研究了一类求解线性方程组的两步迭代方法的收敛加速问题。为实现加速技术，通过在每个子迭代步对应的近似解残差范数上对特定二维子空间进行极小化。详细分析了所提方法的收敛性质。进一步将该方法推广至求解由不适定问题离散化产生的（正则化）正规方程。通过数值实验报告了该方法精确与非精确变体在不同应用领域多个测试问题上的表现性能。