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Randomized and fault-tolerant method of subspace corrections

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Abstract

In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate and use these results to provide sharp estimates for the expected error reduction per iteration. We also study the fault-tolerant features of the randomized successive subspace correction method by rejecting corrections when faults occur and show that the resulting iterative method converges with probability one. In addition, we derive estimates on the expected convergence rate for the fault-tolerant, randomized, subspace correction method.

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Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Authors and Affiliations

  1. Department of Mathematics, Tufts University, Medford, MA, 02155, USA

    Xiaozhe Hu

  2. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Jinchao Xu & Ludmil T. Zikatanov

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  1. Xiaozhe Hu
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  2. Jinchao Xu
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  3. Ludmil T. Zikatanov
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Correspondence to Jinchao Xu.

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The work of Hu was partially supported by NSF (DMS-1620063). The work of Xu and Zikatanov was supported in part by NSF (DMS-1522615)

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Hu, X., Xu, J. & Zikatanov, L.T. Randomized and fault-tolerant method of subspace corrections. Res Math Sci 6, 29 (2019). https://doi.org/10.1007/s40687-019-0187-z

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