A residual-based error bound for the multilinear PageRank vector

The multilinear PageRank vector is the nonnegative and stochastic solution of a system of polynomial equations. In this paper, we consider the case for a third-order tensor in a particular parameter regime. A posteriori error bound is given, which is a bound on the distance between an approximate solution and the real solution, in terms of the residual of the approximate solution. Numerical experiments show that this bound is fairly sharp.