This article introduces new acceleration methods for fixed point iterations. Speed and stability are achieved by alternating the number of mappings to compute step lengths and using them multiple times by cycling. A new type of step length is also proposed with good properties for nonlinear mappings. The methods require no specific adaptation and are especially efficient for high-dimensional problems. Computation uses few objective function evaluations, no matrix inversion and little extra memory. A convergence analysis is followed by seven applications, including gradient descent acceleration for unconstrained optimization. Performances are on par or better than alternatives. The algorithm is available as a stand-alone Julia package and may be downloaded at https://github.com/NicolasL-S/ACX.

翻译：本条为固定点迭代引入了新的加速法。 速度和稳定性的实现是通过交替绘图数来计算台阶长度,并通过自行车进行多次使用。 还提出了新型的阶梯长度,非线性绘图具有良好的特性。 方法不需要具体调整, 并且对高维问题特别有效。 计算很少使用客观功能评价, 没有矩阵反转和少量额外内存。 聚合分析之后有7种应用, 包括不加限制的优化的梯度下降加速。 性能比替代的要好或好。 算法作为独立的Julia 软件包提供, 可以在 https:// github.com/ NicolasL- S/ACX 下载 。