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

2012/10/28 by Daeshik Choi, Choi, Daeshik
Computer Science · Mathematics · Earth and Planetary Sciences · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #Meteorological Phenomena and Simulations

paper · pdf · doi:10.48550/arxiv.1210.7404

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 with the stencil form [-1 2 -1]. Here we show 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/√(2).

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