Titlebook: Newton’s Method: an Updated Approach of Kantorovich’s Theory; José Antonio Ezquerro Fernández,Miguel Ángel Herná Book 2017 Springer Intern

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https://doi.org/10.1007/978-3-319-55976-6Newton’s Method; Kantorovich’s Theory; Semilocal Convergence; Majorizing Sequence; Error Estimates; Order

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José Antonio Ezquerro Fernández,Miguel Ángel HernáUp-to-date account of Kantorovich´s theory for Newton´s method.Starts with a detailed presentation of Kantorovich´s approach and ends with new results and alternative approaches.Contains many numerica

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The classic theory of Kantorovich,le of Banach, and later improved to semilocal quadratic convergence in 1948/49 (the Newton-Kantorovich theorem) [47, 49]. Also in 1949, Mysovskikh [61] gave a much simpler independent proof of semilocal quadratic convergence under slightly different theoretical assumptions, which are exploited in modern Newton algorithms, see [18].

敌意

Convergence conditions on the ,-th derivative of the operator,evious 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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Convergence conditions on the first derivative of the operator,In this chapter, we study the semilocal convergence of Newton’s method under mild differentiability conditions on the operator ..

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