# A modified Newton method for multilinear PageRank

## TL;DR

This paper introduces a modified Newton method for solving polynomial equations in multilinear PageRank, providing convergence guarantees and demonstrating effectiveness through numerical experiments.

## Contribution

It develops a convergence theory for a modified Newton method tailored to multilinear PageRank problems, ensuring monotonic convergence to nonnegative solutions.

## Key findings

- The method guarantees monotonic convergence to the solution.
- Numerical results confirm the method's effectiveness.
- The approach is suitable for specific parameter regimes.

## Abstract

When studying the multilinear PageRank problem, a system of polynomial equations needs to be solved. In this paper, we develop convergence theory for a modified Newton method in a particular parameter regime. The sequence of vectors produced by Newton-like method is monotonically increasing and converges to the nonnegative solution. Numerical results illustrate the effectiveness of this procedure.