Algebraic multigrid smoothing property of Kaczmarz’s relaxation for general rectangular linear systems. (English) Zbl 1188.65036

Summary: 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.


65F10 Iterative numerical methods for linear systems
65F20 Numerical solutions to overdetermined systems, pseudoinverses
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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