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Constructive Approximation

, Volume 48, Issue 3, pp 501–521 | Cite as

Stochastic Subspace Correction in Hilbert Space

  • Michael Griebel
  • Peter Oswald
Article
  • 58 Downloads

Abstract

We consider an incremental approximation method for solving variational problems in infinite-dimensional separable Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is solved. We show that convergence rates for the expectation of the squared error can be guaranteed under weaker conditions than previously established in Griebel and Oswald (Constr Approx 44(1):121–139, 2016).

Keywords

Infinite space splitting Subspace correction Multiplicative Schwarz Block coordinate descent Greedy Randomized Convergence rates Online learning 

Mathematics Subject Classification

65F10 65N22 49M27 

Notes

Acknowledgements

M. Griebel was partially supported by the project EXAHD of the DFG priority program 1648 Software for Exascale Computing (SPPEXA) and by the Sonderforschungsbereich 1060 The Mathematics of Emergent Effects funded by the Deutsche Forschungsgemeinschaft. This paper was written while P. Oswald held a Bonn Research Chair sponsored by the Hausdorff Center for Mathematics at the University of Bonn funded by the Deutsche Forschungsgemeinschaft. He is grateful for this support.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Numerical SimulationUniversität BonnBonnGermany
  2. 2.Fraunhofer Institute for Algorithms and Scientific Computing (SCAI)Schloss BirlinghovenSankt AugustinGermany

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