线性不适定问题的Nesterov加速问题的再探讨

IF 1.8 2区 数学 Q1 MATHEMATICS
Duo Liu , Qin Huang , Qinian Jin
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引用次数: 0

摘要

近年来,为了提高Landweber迭代求解病态问题的效率,引入了Nesterov加速。对于Hilbert空间中的线性不适定问题,分析了Nesterov加速度,并提出了终止迭代的差异原理。然而,现有的方法需要沿两个不同的迭代序列计算残差,从而增加了计算成本。在本文中,我们提出了Nesterov加速的另一种差异原理,该原理消除了计算一个迭代序列的残差的需要,从而将每次迭代的计算时间减少了大约三分之一。我们给出了该方法的收敛性分析,确定了其收敛性和收敛速率。通过数值模拟验证了该方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A revisit on Nesterov acceleration for linear ill-posed problems
In recent years, Nesterov acceleration has been introduced to enhance the efficiency of Landweber iteration for solving ill-posed problems. For linear ill-posed problems in Hilbert spaces, Nesterov acceleration has been analyzed with a discrepancy principle proposed to terminate the iterations. However, the existing approach requires computing residuals along two distinct iterative sequences, resulting in increased computational costs. In this paper, we propose an alternative discrepancy principle for Nesterov acceleration that eliminates the need to compute the residuals for one of the iterative sequences, thereby reducing computational time by approximately one-third per iteration. We provide a convergence analysis of the proposed method, establishing both its convergence and convergence rates. The effectiveness of our approach is demonstrated through numerical simulations.
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来源期刊
Journal of Complexity
Journal of Complexity 工程技术-计算机:理论方法
CiteScore
3.10
自引率
17.60%
发文量
57
审稿时长
>12 weeks
期刊介绍: The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.
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