Hilbert空间中增量型不精确拟牛顿算法的局部收敛性分析
Local Convergence Analysis of Incremental Inexact Quasi-Newton Algorithm in Hilbert Space
DOI: 10.12677/aam.2025.143111, PDF,    科研立项经费支持
作者: 郑 浠, 张 鹏*：牡丹江师范学院数学科学学院，黑龙江 牡丹江
关键词: Hilbert空间；增量型不精确拟牛顿算法；Broyden方法；Hilbert Space； Incremental Inexact Quasi-Newton Algorithm； Broyden Method
摘要: 在图像处理，机器学习和工程学等应用领域中，通常需要处理一些定义在Hilbert空间中的大规模算子方程。为求解这类算子方程及最值问题，构造了一类增量型不精确Broyden方法并证明了该算法的线性收敛和局部超线性收敛性。该算法降低了在处理大规模问题中所产生的储存成本，并通过应用证明了该算法的有效性。
Abstract: In application fields such as image processing, machine learning, and engineering, it is often necessary to solve large-scale operator equations defined in Hilbert spaces. To address such operator equations and optimization problems, a class of incremental inexact Broyden methods has been developed, and the linear convergence as well as local superlinear convergence of this algorithm has been proven. This algorithm reduces the storage costs associated with handling large-scale problems, and its effectiveness has been demonstrated through practical applications.
文章引用：郑浠, 张鹏. Hilbert空间中增量型不精确拟牛顿算法的局部收敛性分析[J]. 应用数学进展, 2025, 14(3): 243-257. https://doi.org/10.12677/aam.2025.143111

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