\noindent Since its publication in 1998, the PageRank model has undergone extensive study and has been adapted for various forms and applications. The goal of this project is to implement a modified version of the Power method for solving the PageRank problem with multiple damping factors, as proposed in \cite{SHEN2022126799}. An algorithm for solving the PageRank problem with multiple damping factors using the Shifted \texttt{GMRES} method will also be proposed, although this has not yet been fully implemented and therefore no numerical results are presented.