An Algebraic Multigrid Preconditioner for a Class of Singular M-Matrices
Elena Virnik · SIAM Journal on Scientific Computing · 2007
We apply algebraic multigrid (AMG) as a preconditioner for solving large singular linear systems of the type $(I-T^T)x=0$ with GMRES. Here, T is assumed to be the transition matrix of a Markov process. Although AMG and GMRES were originally designed for the solution of regular systems, with adequate adaptation their applicability can be extended to problems as described above.