Abstract
The power method with the extrapolation process based on trace (PET)
method was proposed by Tan (2017). It is an extrapolation strategy
derived from the Google matrix. Considering the weighted inner product,
a generalized Arnoldi (GArnoldi) method was constructed by Yin et al.
(2012) for computing PageRank. In this paper, we present a new algorithm
by employing the extrapolation strategy and the GArnoldi method
together. In order to accelerate the convergence speed of PageRank
computations, the weights are changed adaptively with the current
residual corresponding to the approximate vector in each cycle. The new
method is called as GArnoldi-PET algorithm, whose implementation and
convergence are analyzed in detail. Numerical experiments on several
examples are used to illustrate the effectiveness of our proposed
algorithm.