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，其基于将共轭残差型过程从线性方程扩展到非线性方程。根据所实现的不同变体，该主算法与Anderson加速及不精确牛顿方法均有显著相似性。我们从理论证明与实验验证两方面（涵盖从仿真实验到深度学习应用的多类问题）表明，本方法是一种强大的加速迭代算法。