Fast Iterative Solvers for Markov Chains, with Application to Google's PageRank Hans De Sterck Department of Applied Mathematics University of Waterloo, Ontario, Canada joint work with Steve McCormick, John Ruge, Tom Manteuffel, Geoff Sanders (University of Colorado at Boulder), Jamie Pearson (Waterloo) Departamento de Ingeniería Matemática Universidad de Chile, 25 April 2008
37
Embed
Fast Iterative Solvers for Markov Chains, with Application ...hdesterc/websiteW/Data/presentations/pres... · Fast Iterative Solvers for Markov Chains, with Application to Google's
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Fast Iterative Solvers for Markov Chains,with Application to Google's PageRank
Hans De SterckDepartment of Applied Mathematics
University of Waterloo, Ontario, Canada
joint work with Steve McCormick, John Ruge, Tom Manteuffel, GeoffSanders (University of Colorado at Boulder), Jamie Pearson (Waterloo)
Departamento de Ingeniería MatemáticaUniversidad de Chile, 25 April 2008
• “a page has high rank if thesum of the ranks of itsbacklinks is high”(‘The PageRank Citation Ranking:Bringing Order to the Web’ (1998),Page, Brin, Motwani, Winograd)
•
• PageRank = stationary vector ofMarkov chain
• ‘random surfer’, random walk ongraph, robust against ‘spam’
• multilevel method applied to Google’s PageRank withα=0.15 is not faster than power method (SIAM J.Scientific Computing, 2008)
• smoothed multilevel method applied to slowly mixingMarkov chains is much faster than power method(in fact, close to optimal O(n) complexity!) (SIAM J.Scientific Computing, submitted)