Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations

doi:10.1137/16M1080677

Title: Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations

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Abstract

Here, we analyze the convergence of Anderson acceleration when the fixed point map is corrupted with errors. We also consider uniformly bounded errors and stochastic errors with infinite tails. We prove local improvement results which describe the performance of the iteration up to the point where the accuracy of the function evaluation causes the iteration to stagnate. We illustrate the results with examples from neutronics.

Authors:

Toth, Alex ^[1]; Ellis, J. Austin ^[2]; Evans, Tom ^[3]; Hamilton, Steven ^[3]; Kelley, C. T. ^[2]; Pawlowski, Roger ^[1]; Slattery, Stuart ^[3]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
North Carolina State Univ., Raleigh, NC (United States). Dept. of Mathematics
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: 2017-10-26

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1408509

Alternate Identifier(s):: OSTI ID: 1415201

Grant/Contract Number:: [AC05-00OR22725]

Resource Type:: Accepted Manuscript

Journal Name:: SIAM Journal on Scientific Computing

Additional Journal Information:: [ Journal Volume: 39; Journal Issue: 5]; Journal ID: ISSN 1064-8275

Publisher:: SIAM

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; nonlinear equations; Anderson acceleration; local improvement

Citation Formats


                    Toth, Alex, Ellis, J. Austin, Evans, Tom, Hamilton, Steven, Kelley, C. T., Pawlowski, Roger, and Slattery, Stuart. Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations.  United States: N. p., 2017. 
        Web.  doi:10.1137/16M1080677.

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                    Toth, Alex, Ellis, J. Austin, Evans, Tom, Hamilton, Steven, Kelley, C. T., Pawlowski, Roger, & Slattery, Stuart. Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations.  United States.  doi:10.1137/16M1080677.

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                    Toth, Alex, Ellis, J. Austin, Evans, Tom, Hamilton, Steven, Kelley, C. T., Pawlowski, Roger, and Slattery, Stuart. Thu .  
        "Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations".  United States.  doi:10.1137/16M1080677.  https://www.osti.gov/servlets/purl/1408509.

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@article{osti_1408509,

  title        = {Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations},

  author       = {Toth, Alex and Ellis, J. Austin and Evans, Tom and Hamilton, Steven and Kelley, C. T. and Pawlowski, Roger and Slattery, Stuart},

  abstractNote = {Here, we analyze the convergence of Anderson acceleration when the fixed point map is corrupted with errors. We also consider uniformly bounded errors and stochastic errors with infinite tails. We prove local improvement results which describe the performance of the iteration up to the point where the accuracy of the function evaluation causes the iteration to stagnate. We illustrate the results with examples from neutronics.},

  doi          = {10.1137/16M1080677},

  journal      = {SIAM Journal on Scientific Computing},

  number       = [5],

  volume       = [39],

  place        = {United States},

  year         = {2017},

  month        = {10}

}

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DOI: 10.1137/16M1080677

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