Anderson accelerated fixed‐point iteration for multilinear PageRank

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2023-03-28 DOI:10.1002/nla.2499

Fuqi Lai, Wen Li, Xiaofei Peng, Yannan Chen

引用次数: 0

Abstract

In this paper, we apply the Anderson acceleration technique to the existing relaxation fixed‐point iteration for solving the multilinear PageRank. In order to reduce computational cost, we further consider the periodical version of the Anderson acceleration. The convergence of the proposed algorithms is discussed. Numerical experiments on synthetic and real‐world datasets are performed to demonstrate the advantages of the proposed algorithms over the relaxation fixed‐point iteration and the extrapolated shifted fixed‐point method. In particular, we give a strategy for choosing the quasi‐optimal parameters of the associated algorithms when they are applied to solve the test problems with different sizes but the same structure.

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多线性PageRank的Anderson加速不动点迭代

在本文中，我们将Anderson加速技术应用于现有的松弛不动点迭代，以求解多线性PageRank。为了降低计算成本，我们进一步考虑了Anderson加速度的周期性版本。讨论了所提出算法的收敛性。在合成和真实数据集上进行了数值实验，以证明所提出的算法相对于松弛不动点迭代和外推移位不动点方法的优势。特别地，我们给出了一种策略，用于选择相关算法的拟最优参数，当它们被应用于解决具有不同大小但相同结构的测试问题时。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.