===affil2:

===firstname:
Daeshik
===firstname4:

===firstname3:

===lastname2:

===lastname:
Choi
===firstname5:

===affil6:

===lastname3:

===email:
ds77choi@math.washington.edu
===lastname6:

===affil5:

===otherauths:

===lastname4:

===affil4:

===lastname7:

===affil7:

===firstname7:

===postal:
4200 Mary Gates Memorial Dr Ne
Apt P213
Seattle WA 98105
===firstname6:

===ABSTRACT:
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 $1/\sqrt{2}$.
===affil3:

===lastname5:

===affilother:

===title:
A sharp bound on the convergence rate of an aggregation-based algebraic multi-grid method applied to a 1D model problem
===firstname2: