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 for some test problems.

翻译：本文研究加速一类求解线性方程组的双步迭代方法的收敛速度。为实施加速技术，针对每个子迭代计算所得近似解对应的残差范数，在特定二维子空间上进行极小化。详细分析了所提方法的收敛性质。进一步将该方法拓展至求解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，展示了该方法在若干测试问题上的精确与非精确变体的性能表现。