Extrapolation-accelerated aggregation multigrid with block relaxations for GeneRank problems

Abstract

This paper proposes an aggregation multigrid method for computing the GeneRank problem. In this multigrid, the GeneRank transition matrix's formulation is well exploited, and a Block-Jacobi relaxation based on the aggregates, is employed. This block relaxation is well-defined in the multigrid hierarchy and expected to be more efficient than the point-wise version. Besides, the whole method is further accelerated by an extrapolation technique. Numerical experiments demonstrate the potential of this method for computing GeneRank problems.