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Mathematics > Numerical Analysis

arXiv:2306.00325v3 (math)
[Submitted on 1 Jun 2023 (v1) , last revised 30 Mar 2024 (this version, v3)]

Title: NLTGCR: A class of Nonlinear Acceleration Procedures based on Conjugate Residuals

Title: NLTGCR：基于共轭残差的非线性加速算法类

Authors:Huan He, Ziyuan Tang, Shifan Zhao, Yousef Saad, Yuanzhe Xi
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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2306.00325 [math.NA]
  (or arXiv:2306.00325v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2306.00325
Journal reference: SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, pp. 1-827 (2024)
Related DOI: https://doi.org/10.1137/23M1576360

Submission history

From: Huan He [view email]
[v1] Thu, 1 Jun 2023 03:58:57 UTC (6,700 KB)
[v2] Sun, 6 Aug 2023 21:23:59 UTC (6,352 KB)
[v3] Sat, 30 Mar 2024 06:46:44 UTC (6,053 KB)
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