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In this paper, we present a new algorithm by combining the cheap but slow power method with the fast but expensive Arnoldi procedure periodically. The main feature of our method is that a weighted inner product is introduced when using an Arnoldi procedure to construct a basis for a Krylov subspace. Particularly, in each cycle, the weight matrix is changed adaptively according to the residual information obtained from the power iteration, with the aim of accelerating the computation of PageRank problems. The implementation and the convergence analysis of our new method are discussed in detail. Numerical experiments are reported to show the efficiency and convergence behavior of our proposed algorithm. |
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