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On a modified version of the Henrici’s transformation into optimization

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Abstract

The Henrici’s transformation is a method of extrapolation used for solve non-linear equations and systems of equations. By combining the optimal gradient method with a modified Henrici’s transformation, we have already developed a non-linear optimization method. This method is based on the resolution of a linear system at each iteration. In this paper, we improve this method by giving a new formulation that allows us to go from one iteration to the other recursively, which does not require the resolution of an linear system. The demonstration of this new formulation is established and numerical examples are given.

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  1. Ecole Normale Supérieure de Rabat, Université Mohamed V de Rabat, B.P.5118, Rabat, Morocco

    Bouchta Rhanizar

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  1. Bouchta Rhanizar
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Correspondence to Bouchta Rhanizar.

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Rhanizar, B. On a modified version of the Henrici’s transformation into optimization. Numer Algor 90, 507–522 (2022). https://doi.org/10.1007/s11075-021-01196-5

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  • DOI: https://doi.org/10.1007/s11075-021-01196-5

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