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arxiv: 2204.07918 · v2 · pith:E65OG57Nnew · submitted 2022-04-17 · 🧮 math.NA · cs.NA

Convergence analysis of two-grid methods for nonsymmetric positive definite systems

classification 🧮 math.NA cs.NA
keywords convergencemethodstwo-gridanalysissystemsdefinitenonsymmetricpositive
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The convergence theory of multigrid methods for symmetric positive definite systems is well established. For nonsymmetric systems, however, the corresponding theory remains far from mature. Two-grid analysis is fundamental to the design and analysis of multigrid methods. This paper presents a convergence analysis of two-grid methods for nonsymmetric positive definite systems. When the coarse-grid system is solved exactly, we derive a succinct identity for the two-grid convergence factor measured in a smoother-induced norm. More generally, under mild assumptions, we develop a convergence theory for inexact two-grid methods, where convergence is measured in a generic norm.

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