Computational Evaluation of Multi-Iterative Approaches for Solving Graph-Structured Large Linear Systems

We analyze the practical efficiency of multi-iterative techniques for the numerical solution of graph-structured large linear systems. In particular we evaluate the effectiveness of several combinations of coarser-grid operators which preserve the graph structure of the projected matrix at the inner levels and smoothers. We also discuss and evaluate some possible strategies (inverse projection and dense projection) to connect coarser-grid operators and graph-based preconditioners. Our results show that an appropriate choice of adaptive projectors and tree-based preconditioned conjugate gradient methods result in highly effective and robust approaches, that are capable to efficiently solve large-scale, difficult systems, for which the known iterative solvers alone can be rather slow.