We consider inertial iterative schemes for approximating a fixed point of any given non-expansive operator in real Hilbert spaces. We provide new conditions on the inertial factors that ensure weak convergence and depend only on the iteration coefficients. For the special case of the Douglas-Rachford splitting, the conditions boil down to a sufficiently small upper bound on the sequence of inertial factors. Rudimentary numerical results indicate practical usefulness of the proposal.

中文翻译：

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Krasnosel'skiı̆-Mann迭代的新惯性因子

我们考虑惯性迭代方案，用于逼近真实希尔伯特空间中任何给定非膨胀算子的固定点。我们为惯性因子提供了新的条件，以确保收敛性较弱，并且仅取决于迭代系数。对于Douglas-Rachford分裂的特殊情况，条件可以归结为惯性因子序列上足够小的上限。初步的数值结果表明该建议的实用性。