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Schwarz iterative methods: Infinite space splittings

: Griebel, M.; Oswald, P.


Constructive approximation 44 (2016), No.1, pp.121-139
ISSN: 0176-4276 (Print)
ISSN: 1432-0940 (Online)
Journal Article
Fraunhofer SCAI ()

We prove the convergence of greedy and randomized versions of Schwarz iterative methods for solving linear elliptic variational problems based on infinite space splittings of a Hilbert space. For the greedy case, we show a squared error decay rate of O((m+1)−1) for elements of an approximation space A1 related to the underlying splitting. For the randomized case, we show an expected squared error decay rate of O((m+1)−1) on a class Aπ∞⊂A1 depending on the probability distribution.