A modified multi-step splitting iteration and its variants for computing PageRank

In recent years, the PageRank algorithm has garnered significant attention due to its crucial role in search engine technologies and its applications across various scientific fields. It is well-known that the power method is a classical method for computing PageRank. However, there is a pressing demand for alternative approaches that can address its limitations and enhance its efficiency. Specifically, the power method converges very slowly when the damping factor is close to 1. To address this challenge, this paper introduces a modified multi-step splitting iteration approach for accelerating PageRank computations. Furthermore, we present two variants for computing PageRank, which are variants of the modified multi-step splitting iteration approach, specifically utilizing the thick restarted Arnoldi and adaptively accelerated Arnoldi methods. We provide detailed discussions on the construction and theoretical convergence results of these two approaches. Extensive experiments using large test matrices demonstrate the significant performance improvements achieved by our proposed algorithms.