Recently, the authors (Dong et al. in J Global Optim 73(4):801–824, 2019) introduced the multi-step inertial Krasnosel’skiǐ–Mann iteration, where the inertial parameters involve the iterative sequence. Therefore, one has to compute the inertial parameters per iteration. The aim of this article is to present two kinds of inertial parameter arrays which do not depend on the iterative sequence. We first introduce a general Krasnosel’skiǐ–Mann iteration on the affine hull of orbits, based on which one inertial parameter array is presented. Second, we investigate the other inertial parameter array by introducing a modified Krasnosel’skii-Mann iteration. The convergence of the modified Krasnosel’skiǐ–Mann iteration is shown using an exhaustive convergence analysis and the running-average iteration-complexity bound is provided. Finally, we give two numerical examples to illustrate that the multi-step inertial Krasnosel’skiǐ–Mann iteration with inertial parameters proposed in this article behaves better than that with inertial parameters given in [10].

最近，作者（Dong et al. in J Global Optim 73(4):801–824, 2019）介绍了多步惯性 Krasnosel'skiǐ–Mann 迭代，其中惯性参数涉及迭代序列。因此，必须计算每次迭代的惯性参数。本文的目的是提出两种不依赖于迭代序列的惯性参数数组。我们首先介绍了轨道仿射壳上的一般 Krasnosel'skiǐ-Mann 迭代，并在此基础上提出了一个惯性参数阵列。其次，我们通过引入改进的 Krasnosel'skii-Mann 迭代来研究其他惯性参数数组。修改后的 Krasnosel'skiǐ–Mann 迭代的收敛性使用详尽的收敛分析显示，并提供了运行平均迭代复杂度界限。最后，