nlTGCR：基于共轭残差的一类非线性加速程序

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-02-29 DOI:10.1137/23m1576360

Huan He, Ziyuan Tang, Shifan Zhao, Yousef Saad, Yuanzhe Xi

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引用次数: 0

摘要

SIAM 矩阵分析与应用期刊》，第 45 卷，第 1 期，第 712-743 页，2024 年 3 月。摘要本文基于从线性方程扩展到非线性方程的共轭残差型程序，开发了一类新的非线性加速算法。主要算法与安德森加速法以及不精确牛顿法有很强的相似性--这取决于采用哪种变体。我们从理论上证明了我们的方法是一种强大的加速迭代算法，并在从模拟实验到深度学习应用的各种问题上进行了实验验证。代码见 https://github.com/Data-driven-numerical-methods/Nonlinear-Truncated-Conjugate-Residual。

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nlTGCR: A Class of Nonlinear Acceleration Procedures Based on Conjugate Residuals

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.

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.