Multigraph Iterative Methods

Randolph E. Bank
University of California at San Diego, USA


      The class of Multigraph Iterative Methods is obtained by examining the close connection between classical multigrid and hierarchical basis methods and incomplete LU decomposition. Using this connection, one is able to formally generalize both hierarchical basis and multigrid methods to the case of gen- eral sparse matrix graphs. These correspond to ILU methods in which certain fill-in edges are allowed. In this talk, I will discuss the derivation of the methods, and present some recent numerical results.