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 new multi-step splitting iteration approach for accelerating PageRank computations. Furthermore, we present two new approaches for computating PageRank, which are modifications of the new multi-step splitting iteration approach, specifically utilizing the thick restarted Arnoldi and generalized 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.

翻译：近年来，PageRank算法因其在搜索引擎技术中的关键作用及其在多个科学领域的应用而受到广泛关注。众所周知，幂法是计算PageRank的经典方法。然而，迫切需要能够克服其局限性并提升效率的替代方案。具体而言，当阻尼因子接近1时，幂法收敛速度极慢。为应对这一挑战，本文提出了一种新的多步分裂迭代方法，用于加速PageRank计算。此外，我们提出了两种计算PageRank的新方法，这些方法是对新多步分裂迭代方法的改进，具体利用了厚重启Arnoldi方法和广义Arnoldi方法。我们详细讨论了这两种方法的构造及理论收敛结果。使用大型测试矩阵的大量实验表明，我们提出的算法在性能上取得了显著提升。