Výsledky vyhledávání - Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms

Affine conjugate adaptive Newton methods for nonlinear elastomechanics Autor Weiser, Martin, Deuflhard, Peter, Erdmann, Bodo

“…The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity…”
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Superlinear Convergence of Affine-Scaling Interior-Point Newton Methods for Infinite-Dimensional Nonlinear Problems with Pointwise Bounds Autor Ulbrich, Michael, Ulbrich, Stefan

“…We develop and analyze a superlinearly convergent affine-scaling interior-point Newton method for infinite-dimensional problems with pointwise bounds in Lp-space…”
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An adaptive model order reduction with Quasi-Newton method for nonlinear dynamical problems Autor Nigro, P. S. B., Anndif, M, Teixeira, Y., Pimenta, P. M., Wriggers, P.

“…). It is supported by a new adaptive strategy, which analyzes the error and the convergence rate for nonlinear dynamical problems…”
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Bridging proper orthogonal decomposition methods and augmented Newton–Krylov algorithms: An adaptive model order reduction for highly nonlinear mechanical problems Autor Kerfriden, P., Gosselet, P., Adhikari, S., Bordas, S.P.A.

“… This bridge is used to derive an efficient algorithm to correct, “on-the-fly”, the reduced order modelling of highly nonlinear problems undergoing strong topological changes…”
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Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems Autor Kerfriden, Pierre, Gosselet, Pierre, Adhikari, Sondipon, Bordas, Stéphane

“… This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes…”
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On the convergence of Newton-type methods using recurrent functions Autor Argyros, Ioannis K., Hilout, Saïd

“… Math. Comput. 136 (2003), pp. 215-228; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in Nonlinear Functional Analysis and Applications, L.B. Rall, ed…”
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On Newton-like methods of “bounded deterioration” using recurrent functions Autor Argyros, Ioannis K., Hilout, Saïd

“… or weaker hypotheses than before (Argyros, Acta Math. Sin. (Engl. Ser.), 23:2087–2096, 2007; Deuflhard, Newton methods for nonlinear problems…”
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