Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 53, Issue 2, Pages 805-819Publisher
SIAM PUBLICATIONS
DOI: 10.1137/130919398
Keywords
nonlinear equations; Anderson acceleration; local convergence
Categories
Funding
- Consortium for Advanced Simulation of Light Water Reactors
- Energy Innovation Hub for Modeling and Simulation of Nuclear Reactors under U.S. Department of Energy [DE-AC05-00OR22725]
- National Science Foundation [DMS-1406349, CDI-0941253, OCI-0749320, SI2-SSE-1339844]
- Army Research Office [W911NF-11-1-0367, W911NF-07-1-0112]
- Direct For Computer & Info Scie & Enginr
- Office of Advanced Cyberinfrastructure (OAC) [1339844] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1406349] Funding Source: National Science Foundation
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Anderson(m) is a method for acceleration of fixed point iteration which stores m + 1 prior evaluations of the fixed point map and computes the new iteration as a linear combination of those evaluations. Anderson(0) is fixed point iteration. In this paper we show that Anderson(m) is locally r-linearly convergent if the fixed point map is a contraction and the coefficients in the linear combination remain bounded. Without assumptions on the coefficients, we prove q-linear convergence of Anderson(1) and, in the case of linear problems, Anderson(m). We observe that the optimization problem for the coefficients can be formulated and solved in nonstandard ways and report on numerical experiments which illustrate the ideas.
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