Anderson($m_0$) extrapolation, an accelerator to a fixed-point iteration, stores $m_0+1$ 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($m_0$) acceleration becomes expensive with the parameter $m_0$ increasing, thus $m_0$ 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.

中文翻译：

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用于计算PageRank的Arnoldi-Inout方法的Anderson加速

安德森（${米}_0$）外推（定点迭代的加速器）存储 ${米}_0+\mathrm{1个}$定点迭代的先前评估，并将这些评估的线性组合作为新的迭代进行计算。安德森的计算成本（${米}_0$）加速因参数而变得昂贵 ${米}_0$ 增加，因此 ${米}_0$是大多数实践中的常见选择。为了改进PageRank问题的计算，本文通过在Arnoldi-Inout方法内以周期性间隔应用Anderson（1）外推法开发了一种新方法。新方法称为AIOA方法。详细讨论了AIOA方法的收敛性分析。提出了若干PageRank问题的数值结果，以说明我们提出的方法的有效性。