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Keywords = Arnoldi-Inout method

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13 pages, 7633 KB  
Article
Anderson Acceleration of the Arnoldi-Inout Method for Computing PageRank
by Xia Tang, Chun Wen, Xian-Ming Gu and Zhao-Li Shen
Symmetry 2021, 13(4), 636; https://doi.org/10.3390/sym13040636 - 10 Apr 2021
Cited by 1 | Viewed by 2485
Abstract
Anderson(m0) extrapolation, an accelerator to a fixed-point iteration, stores m0+1 prior evaluations of the fixed-point iteration and computes a linear combination of those evaluations as a new iteration. The computational cost of the Anderson(m0) [...] Read more.
Anderson(m0) extrapolation, an accelerator to a fixed-point iteration, stores m0+1 prior evaluations of the fixed-point iteration and computes a linear combination of those evaluations as a new iteration. The computational cost of the Anderson(m0) acceleration becomes expensive with the parameter m0 increasing, thus m0 is a common choice in most practice. In this paper, with the aim of improving the computations of PageRank problems, a new method was developed by applying Anderson(1) extrapolation at periodic intervals within the Arnoldi-Inout method. The new method is called the AIOA method. Convergence analysis of the AIOA method is discussed in detail. Numerical results on several PageRank problems are presented to illustrate the effectiveness of our proposed method. Full article
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