Solving linear systems with boundary conditions using heat kernel pagerank

Abstract

We present an efficient algorithm for solving linear systems with a boundary condition by computing the Green's function of a connected induced subgraph S of a graph. Different from previous linear solvers, we introduce the method of using the Dirichlet heat kernel pagerank of the induced graph to approximate the solution to diagonally dominant linear systems satisfying given boundary conditions. Our algorithm runs in time Õ(1), with the assumption that a unit time allows a step in a random walk or a sampling of a specified distribution, where the big-O term depends on the error term and the boundary condition. © 2013 Springer International Publishing.