Schwarz iterative methods: Infinite space splittings
Schwarz iterative methods: Infinite space splittings
View/Date of Publication
12.2014Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11919
Abstract
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.
Subjects
infinite space splitting, subspace correction, multiplicative Schwarz, block coordinate descent, greedy, randomized, convergence rates
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/s00365-015-9318-yPart of Series
INS Preprints ; 1413Griebel, Michael; Oswald, Peter: Schwarz iterative methods: Infinite space splittings. In: INS Preprints, 1413.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11919
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11919
@unpublished{handle:20.500.11811/11919,
author = {{Michael Griebel} and {Peter Oswald}},
title = {Schwarz iterative methods: Infinite space splittings},
publisher = {Institut für Numerische Simulation (INS)},
year = 2014,
month = dec,
INS Preprints},
volume = 1413,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/11919}
}
author = {{Michael Griebel} and {Peter Oswald}},
title = {Schwarz iterative methods: Infinite space splittings},
publisher = {Institut für Numerische Simulation (INS)},
year = 2014,
month = dec,
INS Preprints},
volume = 1413,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/11919}
}
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