This paper develops a new class of nonlinear acceleration algorithms based on extending conjugate residual-type procedures from linear to nonlinear equations. The main algorithm has strong similarities with Anderson acceleration as well as with inexact Newton methods - depending on which variant is implemented. We prove theoretically and verify experimentally, on a variety of problems from simulation experiments to deep learning applications, that our method is a powerful accelerated iterative algorithm.

翻译：本文发展了一类新的非线性加速算法，其核心在于将共轭残差类方法从线性方程推广至非线性方程。根据所实现变体的不同，主算法与安德森加速及非精确牛顿法均具有高度相似性。我们从理论上证明并在实验上验证（涵盖从仿真实验到深度学习应用的多类问题），该方法是一种强大的加速迭代算法。