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Old and new convergence proofs for multigrid methods. (English) Zbl 0788.65108
Iserles, A. (ed.), Acta Numerica 1993. Cambridge: Cambridge University Press. 285-326 (1993).
The article reviews old and new developments of multigrid methods for the solution of large systems of equations arising from the discretization of partial differential equations. For self-adjoint and coercive linear elliptic boundary value problems the convergence theory is presented. A convergence theory for the V-cycle and general multiplicative methods is given. Further additive multilevel methods are discussed.
For the entire collection see [Zbl 0777.00039].

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
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