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We propose a globalization method for <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\textsf{AA}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>AA<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to improve stability and achieve unified global and local convergence. Unlike existing <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\textsf{AA}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>AA<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> globalization approaches that rely on safeguarding operations and might hinder fast local convergence, we adopt a nonmonotone trust-region framework and introduce an adaptive quadratic regularization together with a tailored acceptance mechanism. We prove global convergence and show that our algorithm attains the same local convergence as <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\textsf{AA}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>AA<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> under appropriate assumptions. The effectiveness of our method is demonstrated in several numerical experiments.<\/jats:p>","DOI":"10.1007\/s10915-023-02231-4","type":"journal-article","created":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T06:02:14Z","timestamp":1684476134000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Nonmonotone Globalization for Anderson Acceleration via Adaptive Regularization"],"prefix":"10.1007","volume":"96","author":[{"given":"Wenqing","family":"Ouyang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiong","family":"Tao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andre","family":"Milzarek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0158-7670","authenticated-orcid":false,"given":"Bailin","family":"Deng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,18]]},"reference":[{"key":"2231_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jcp.2017.06.031","volume":"347","author":"H An","year":"2017","unstructured":"An, H., Jia, X., Walker, H.F.: Anderson acceleration and application to the three-temperature energy equations. 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