Abstract In this paper, we revisit the multilinear PageRank problem. Under the framework of tensor, we establish several new and tighter uniqueness conditions for the multilinear PageRank vector. Meanwhile, a refined error bound for the inverse iteration as well as the new perturbation bounds under different norms, which improve the existing ones in the current literature, are developed with feasible computations. Several numerical examples are given to validate the significant effectiveness of the proposed bounds.

中文翻译：

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多线性 PageRank：唯一性、误差界限和扰动分析

摘要 在本文中，我们重新审视了多线性 PageRank 问题。在张量的框架下，我们为多线性 PageRank 向量建立了几个新的更严格的唯一性条件。同时，通过可行的计算开发了逆迭代的细化误差界限以及不同范数下的新扰动界限，这些界限改进了现有文献中的现有扰动界限。给出了几个数值例子来验证所提出的界限的显着有效性。