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An autoadaptative limited memory Broyden’s method to solve systems of nonlinear equations

Mohammed Ziani 1 Frédéric Guyomarc'H 2
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
2 DART - Contributions of the Data parallelism to real time
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
Abstract : We propose a new Broyden-like method that we call autoadaptative limited memory method. Unlike classical limited memory method, we do not need to set any parameters such as the maximal size, that solver can use. In fact, the autoadaptative algorithm automatically increases the approximate subspace when the convergence rate decreases. The convergence of this algorithm is superlinear under classical hypothesis. A few numerical results with well-known benchmarks functions are also provided and show the efficiency of the method.
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Mohammed Ziani, Frédéric Guyomarc'H. An autoadaptative limited memory Broyden’s method to solve systems of nonlinear equations. Applied Mathematics and Computation, Elsevier, 2008, 205 (1), ⟨10.1016/j.amc.2008.06.047⟩. ⟨hal-01580904⟩

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