Daeshik Choi
Analysis of a Two-grid Aggregation-based Algebraic Multigrid Method on centrosymmetric and symmetric positive-definite matrices

Southern Illinois University Edwardsville
Dept of Mathematics and Statistics
P O Box 1653
Edwardsville
IL
62026-1653
dchoi@siue.edu

For a given matrix $A$ which is a centrosymmetric and symmetric positive-definite matrix with identical diagonal entries, we analyze the $A$ -norm of errors of a two-grid aggregation-based algebraic multigrid method to the linear system $Ax=b$ . More precisely, we will show that the $A$ -norm of the error at each step is reduced by a constant which can be computed by solving a generalized symmetric positive-definite eigenvalue problem of size $n/4$ , where $n$ is the size of $A$ .