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The result shows that the leading term in the residual is improved by the gain in the optimization problem, but at the cost of additional higher order terms that can be significant when the residual is large. We perform numerical tests that illustrate the theory, and show that a 2-stage choice of Anderson depth can be advantageous. We also consider Anderson acceleration applied to the Newton iteration for the Boussinesq equations, and observe that the acceleration allows the Newton iteration to converge for significantly higher Rayleigh numbers that it could without acceleration, even with a standard line search.<\/jats:p>","DOI":"10.1515\/jnma-2020-0067","type":"journal-article","created":{"date-parts":[[2020,11,30]],"date-time":"2020-11-30T20:47:20Z","timestamp":1606769240000},"page":"323-341","source":"Crossref","is-referenced-by-count":13,"title":["Acceleration of nonlinear solvers for natural convection problems"],"prefix":"10.1515","volume":"29","author":[{"given":"Sara","family":"Pollock","sequence":"first","affiliation":[{"name":"Department of Mathematics , University of Florida , Gainesville , FL 32611 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leo G.","family":"Rebholz","sequence":"additional","affiliation":[{"name":"School of Mathematical and Statistical Sciences , Clemson University , Clemson , SC 29634 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengying","family":"Xiao","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics , University of West Florida , Pensacola , FL 32514 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2021,12,2]]},"reference":[{"key":"2023010208482904906_j_jnma-2020-0067_ref_001","doi-asserted-by":"crossref","unstructured":"H. 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