Volume 29, pp. 150-162, 2007-2008.

Algebraic multigrid smoothing property of Kaczmarz's relaxation for general rectangular linear systems

Constantin Popa

Abstract

In this paper we analyze the smoothing property from classical Algebraic Multigrid theory, for general rectangular systems of linear equations. We prove it for Kaczmarz's projection algorithm in the consistent case and obtain in this way a generalization of the classical well-known result by A. Brandt. We then extend this result for the Kaczmarz Extended algorithm in the inconsistent case.

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Key words

algebraic multigrid, smoothing property, Kaczmarz relaxation, inconsistent least squares problems

AMS subject classifications

65F10, 65F20, 65N55

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