Abstract
According to Polyak [66], Kantorovich proved in 1939 the semilocal convergence of Newton’s method [46] on the basis of the contraction mapping principle 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].
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Ezquerro Fernández, J.A., Hernández Verón, M.Á. (2017). The classic theory of Kantorovich. 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_1
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DOI: https://doi.org/10.1007/978-3-319-55976-6_1
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