Abstract
Following with the idea of improving the applicability of Newton’s method, in this chapter, we extend the semilocal convergence results seen in the previous chapter for Newton’s method under conditions on the second derivative of the operator involved. So, we establish semilocal convergence results for Newton’s method under conditions on derivatives of the operator of order greater than two.
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Ezquerro Fernández, J.A., Hernández Verón, M.Á. (2017). Convergence conditions on the k-th derivative of the operator. In: Newton’s Method: an Updated Approach of Kantorovich’s Theory. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55976-6_3
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DOI: https://doi.org/10.1007/978-3-319-55976-6_3
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-55975-9
Online ISBN: 978-3-319-55976-6
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