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===firstname:
Meng-Huo (Alan)
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===firstname3:

===lastname2:

===lastname:
Chen
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===lastname3:

===email:
mchen01@uw.edu
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===affil5:

===otherauths:

===lastname4:

===affil4:

===lastname7:

===affil7:

===firstname7:

===postal:
Department of Applied Mathematics, 
University of Washington, 
Guggenheim Hall #414, Box 352420, 
Seattle, WA 98195-2420 USA 
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===ABSTRACT:
We show that a pairwise aggregation-based algebraic 2-grid method,
applied to the linear system $Ax = b$ arising from a 1D model problem for Poisson's equation with Dirichlet boundary conditions, reduces the $A$-norm of the error at each step by at least the factor $\sqrt{5/8}$. We then generalize this result to problems with the same eigenvectors but different eigenvalues from the model problem, and also to problems with different eigenvectors that are especially well-suited to the method. Finally, we discuss the reduction in the A-norm of the error when the 2-grid method is replaced by a multigrid V-cycle and indicate that conjugate gradient acceleration is required in order to improve the degraded performance of multigrid V-cycle.
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===affilother:

===title:
Analysis Of an Aggregation-Based Algebraic Multigrid Methods On Matrices Related to a 1D Model Problem
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