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nlTGCR: A Class of Nonlinear Acceleration Procedures Based on Conjugate Residuals
SIAM Journal on Matrix Analysis and Applications ( IF 1.5 ) Pub Date : 2024-02-29 , DOI: 10.1137/23m1576360 Huan He 1 , Ziyuan Tang 2 , Shifan Zhao 3 , Yousef Saad 2 , Yuanzhe Xi 3
SIAM Journal on Matrix Analysis and Applications ( IF 1.5 ) Pub Date : 2024-02-29 , DOI: 10.1137/23m1576360 Huan He 1 , Ziyuan Tang 2 , Shifan Zhao 3 , Yousef Saad 2 , Yuanzhe Xi 3
Affiliation
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 712-743, March 2024.
Abstract. 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. The code is available at https://github.com/Data-driven-numerical-methods/Nonlinear-Truncated-Conjugate-Residual.
中文翻译：
nlTGCR：一类基于共轭残差的非线性加速程序
《SIAM 矩阵分析与应用杂志》，第 45 卷，第 1 期，第 712-743 页，2024 年 3 月。
摘要。本文基于将共轭残差类型过程从线性方程扩展到非线性方程，开发了一类新型非线性加速算法。主要算法与安德森加速以及不精确的牛顿方法有很强的相似性——具体取决于实现的变体。我们从理论上证明并通过实验验证了从模拟实验到深度学习应用的各种问题，我们的方法是一种强大的加速迭代算法。该代码位于 https://github.com/Data-driven-numeric-methods/Nonlinear-Truncated-Conjugate-Residual。
更新日期：2024-02-29
Abstract. 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. The code is available at https://github.com/Data-driven-numerical-methods/Nonlinear-Truncated-Conjugate-Residual.
中文翻译：
nlTGCR：一类基于共轭残差的非线性加速程序
《SIAM 矩阵分析与应用杂志》，第 45 卷，第 1 期，第 712-743 页，2024 年 3 月。
摘要。本文基于将共轭残差类型过程从线性方程扩展到非线性方程，开发了一类新型非线性加速算法。主要算法与安德森加速以及不精确的牛顿方法有很强的相似性——具体取决于实现的变体。我们从理论上证明并通过实验验证了从模拟实验到深度学习应用的各种问题，我们的方法是一种强大的加速迭代算法。该代码位于 https://github.com/Data-driven-numeric-methods/Nonlinear-Truncated-Conjugate-Residual。
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