\documentclass[11pt]{article} \usepackage[margin=1.2in]{geometry} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage[T1]{fontenc} \usepackage{fourier} \usepackage{amsthm} \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{latexsym} \usepackage{graphicx} \usepackage{float} \usepackage{etoolbox} \usepackage{hyperref} \usepackage{tikz} \usepackage{lipsum} \usepackage{algorithm} \usepackage{algpseudocode} \usepackage{mathtools} \usepackage{nccmath} \usepackage[most]{tcolorbox} \newtcolorbox[auto counter]{problem}[1][]{% enhanced, breakable, colback=white, colbacktitle=white, coltitle=black, fonttitle=\bfseries, boxrule=.6pt, titlerule=.2pt, toptitle=3pt, bottomtitle=3pt, title=GitHub repository of this project} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\C}{\mathbb{C}} % add counters \title{Methods for solving PageRank with multiple damping factors} \author{Luca Lombardo} \date{} \begin{document} \maketitle \begin{abstract} \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. \end{abstract} \tableofcontents \clearpage \include{intro.tex} \include{shifted.tex} \include{shift_GMRES.tex} \include{num.tex} \clearpage \bibliographystyle{unsrt} \bibliography{ref} \nocite{*} \end{document}