Title: Parameterized Matrix Equations and PageRank Speaker: Paul G. Constantine and David F. Gleich, Stanford University Date/Time: Thursday, August 6, 2009, 11:00 am (MST) Location: CSRI Building, Room 90 (NM), 915/S101 (CA) Brief Abstract: Parameterized matrix equations are linear systems where the coefficient matrix and/or right hand side depend on one or more parameters. These systems arise in a wide range of engineering applications and are fundamental to the study of uncertainty quantification. We employ polynomial approximation techniques -- known in the context of numerical PDEs as spectral methods -- to approximate the vector-valued function that satisfies the parameterized equation. We present theory and error estimates for such procedures applied to equations that depend on a single parameter, and we allude to the multi-parameter case. Next, we focus on one particular parameterized system: the PageRank equations used to rank the nodes of a directed graph. Here, the parameter is the teleportation coefficient often denoted alpha. On the web, one interpretation of PageRank is given by the random surfer model. Using the parameterized equation techniques allows us to compute PageRank results reflecting aggregate behavior about browsing the web. A side effect is a new sensitivity measure that appears useful in identifying spam pages.CSRI POC: Tamara Kolda, (925) 294-2234 |