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Newton-Kantorovich Method and Its Global Convergence

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Abstract

In 1948, L. V. Kantorovich extended the Newton method for solving nonlinear equations to functional spaces. This event cannot be overestimated: the Newton-Kantorovich method became a powerful tool in numerical analysis as well as in pure mathematics. We address basic ideas of the method in historical perspective and focus on some recent applications and extensions of the method and some approaches to overcoming its local ture. Bibliography: 56 titles.

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Authors and Affiliations

  1. Institute of Control Sciences, Moscow, Russia

    B. T. Polyak

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  1. B. T. Polyak
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 256–274.

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Polyak, B.T. Newton-Kantorovich Method and Its Global Convergence. J Math Sci 133, 1513–1523 (2006). https://doi.org/10.1007/s10958-006-0066-1

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  • DOI: https://doi.org/10.1007/s10958-006-0066-1

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