Geodesic
An inverse free Broyden's method for solving equations
Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1.

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Based on a center-Lipschitz-type condition and our idea of the restricted convergence domain, we present a new semi-local convergence analysis for an inverse free Broyden's method (BM) in order to approximate a locally unique solution of an equation in a Hilbert space setting. The operators involved have regularly continuous divided differences. This way we provide weaker sufficient semi-local convergence conditions, tighter error bounds, and a more precise information on the location of the solution. Hence, our approach extends the applicability of BM under the same hypotheses as before. Finally, we consider some special cases.
Publié le :
DOI : 10.30755/NSJOM.07759
Classification : 65J15, 47H17, 47J05, 49M15
Keywords: Broyden's method, Hilbert space, semi-local convergence, regularly continuous divided differences 
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Ioannis K. Argyros; Santhosh George. An inverse free Broyden's method for solving equations. Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1. doi : 10.30755/NSJOM.07759. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.07759/

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