  This paper presents a deterministic linear time complexity IDE-SimRank method
to approximately compute SimRank with proved error bound. SimRank is a
well-known similarity measure between graph vertices which relies on graph
topology only and is built on intuition that "two objects are similar if they
are related to similar objects". The fixed point equation for direct SimRank
computation is the discrete Lyapunov equation with specific diagonal matrix in
the right hand side. The proposed method is based on estimation of this
diagonal matrix with GMRES and use this estimation to compute singe-source and
single pairs queries. These computations are executed with the part of series
converging to the discrete Lyapunov equation solution.
