skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Journal Article · · SIAM Journal on Scientific Computing
DOI:https://doi.org/10.1137/16M1080677· OSTI ID:1408509
 [1];  [2];  [3];  [3];  [2];  [1];  [3]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. North Carolina State Univ., Raleigh, NC (United States). Dept. of Mathematics
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1408509
Alternate ID(s):
OSTI ID: 1415201
Journal Information:
SIAM Journal on Scientific Computing, Vol. 39, Issue 5; ISSN 1064-8275
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 23 works
Citation information provided by
Web of Science

References (24)

Application of the Mesh Independence Principle to Mesh Refinement Strategies journal December 1987
A Mesh-Independence Principle for Operator Equations and Their Discretizations journal February 1986
Iterative Procedures for Nonlinear Integral Equations journal October 1965
Design and Application of a Gradient-Weighted Moving Finite Element Code I: in One Dimension journal May 1998
Mesh Independence of Matrix-Free Methods for Path Following journal January 2000
MOOSE: A parallel computational framework for coupled systems of nonlinear equations journal October 2009
An assessment of coupling algorithms for nuclear reactor core physics simulations journal April 2016
Mesh Independence of Newton-like Methods for Infinite Dimensional Problems journal December 1991
Application of the Jacobian-Free Newton-Krylov Method to Nonlinear Acceleration of Transport Source Iteration in Slab Geometry journal February 2011
A black-box self-consistent field convergence algorithm: One step closer journal January 2002
Elliptic Preconditioner for Accelerating the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory journal January 2013
An accelerated Picard method for nonlinear systems related to variably saturated flow journal March 2012
Nonlinear Krylov and moving nodes in the method of lines journal November 2005
Krylov Subspace Acceleration of Nonlinear Multigrid with Application to Recirculating Flows journal January 2000
Convergence acceleration of iterative sequences. the case of scf iteration journal July 1980
ImprovedSCF convergence acceleration journal January 1982
An analysis for the DIIS acceleration method used in quantum chemistry calculations journal August 2011
Flexible Inner-Outer Krylov Subspace Methods journal January 2002
Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing journal January 2003
Recent computational developments in Krylov subspace methods for linear systems journal January 2007
Convergence Analysis for Anderson Acceleration journal January 2015
Anderson Acceleration for Fixed-Point Iterations journal January 2011
Newton's Method for Monte Carlo--Based Residuals journal January 2015
Hybrid Deterministic/Monte Carlo Neutronics journal January 2013

Cited By (1)

Numerical methods for nonlinear equations journal May 2018