Anderson acceleration based on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e414" altimg="si4.svg"><mml:msup><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msup></mml:math> Sobolev norm for contractive and noncontractive fixed-point operators
نویسندگان
چکیده
Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to sequence functions and modify norm in its internal optimization problem H−s norm, some positive integer s, bias it towards low-frequency spectral content residual. We analyze by quantifying improvement over Picard iteration. find that based on H−2 well-suited solve operators derived from second-order elliptic differential operators, including Helmholtz equation.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2022
ISSN: ['0377-0427', '1879-1778', '0771-050X']
DOI: https://doi.org/10.1016/j.cam.2021.113844