Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 43, Issue 5, Pages S1-S20Publisher
SIAM PUBLICATIONS
DOI: 10.1137/20M132938X
Keywords
Key words; nonsmooth equatioins; Anderson acceleration; integral equations; nonlinear equations; fixed-point problems
Categories
Funding
- NSF foundation of China [11871178, 61773136]
- Hong Kong Research Grant Council [15300219]
- Army Research Office [W911NF-16-1-0504]
- National Science Foundation [OAC-1740309, DMS-1745654, DMS-1906446]
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This research proves the convergence of Anderson acceleration for a class of nonsmooth fixed-point problems, where the nonlinearities can be decomposed into a smooth contractive part and a nonsmooth part with a small Lipschitz constant. These problems arise from the composition of completely continuous integral operators and pointwise nonsmooth functions, and the results are illustrated with two examples.
We prove convergence of Anderson acceleration for a class of nonsmooth fixed-point problems for which the nonlinearities can be split into a smooth contractive part and a nonsmooth part which has a small Lipschitz constant. These problems arise from compositions of completely continuous integral operators and pointwise nonsmooth functions. We illustrate the results with two examples.
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