Krasnoselskii–Mann Iterations: Inertia, Perturbations and Approximation
本文系统研究了一类结合松弛与不同惯性（加速）原理的不动点迭代族，分析了保证其弱收敛、强收敛和线性收敛的假设条件，并证明这些方法在极弱假设下对计算误差、有意偏差及正则化等扰动具有鲁棒性。数值实验展示了其在图像修复和电力市场中的应用趋势。
Abstract This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unified and insightful analysis of the hypotheses that ensure their weak, strong and linear convergence, either matching or improving previous results obtained by analysing particular cases separately. We also show that these methods are robust with respect to different kinds of perturbations–which may come from computational errors, intentional deviations, as well as regularisation or approximation schemes–under surprisingly weak assumptions. Although we mostly focus on theoretical aspects, numerical illustrations in image inpainting and electricity production markets reveal possible trends in the behaviour of these types of methods.