Daeshik Choi
A sharp bound on the convergence rate of an aggregation-based algebraic multi-grid method applied to a 1D model problem

4200 Mary Gates Memorial Dr Ne
Apt P213
Seattle WA 98105
ds77choi@math.washington.edu

We consider the linear system $Ax=b$ arising from one-dimensional Poisson's equation with Dirichlet boundary conditions, where $A$ is the square matrix having the stencil form $\begin{bmatrix}-1 & 2 & -1\end{bmatrix}$ . Here we show, using some properties of centrosymmetric matrices, that a pairwise aggregation-based algebraic 2-grid method reduces the $A$ -norm of the error at each step by at least the factor $1/\sqrt{2}$ .