乐胖代购免代理版

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We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least\u2010squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed\u2010point iterations arising from the Richardson's scheme to solve linear systems with open\u2010source benchmark matrices with various preconditioners and (ii) non\u2010linear deterministic fixed\u2010point iterations arising from non\u2010linear time\u2010dependent Boltzmann equations.<\/jats:p>","DOI":"10.1002\/nla.2562","type":"journal-article","created":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T06:40:46Z","timestamp":1715323246000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Anderson acceleration with approximate calculations: Applications to scientific computing"],"prefix":"10.1002","volume":"31","author":[{"given":"Massimiliano","family":"Lupo Pasini","sequence":"first","affiliation":[{"name":"Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak Ridge Tennessee USA"}]},{"given":"M. Paul","family":"Laiu","sequence":"additional","affiliation":[{"name":"Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge Tennessee USA"}]}],"member":"311","published-online":{"date-parts":[[2024,5,9]]},"reference":[{"unstructured":"ChenK VuikC.Non\u2010stationary Anderson acceleration with optimized damping. 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