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Global convergence of Newton-Like methods

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Part of the Lecture Notes in Mathematics book series (LNM,volume 909)

Abstract

In this paper we consider a general class of Newton-like methods for calculating the solution of n nonlinear equations in n variables, which are continously differentiable.

Assuming nonsingularity and Lipschitz continuity of the jacobian (the matrix of first partial derivatives of the system) on a certain level set, then we can derive a global convergence theorem for iterative methods in the given class.

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References

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© 1982 Springer-Verlag

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Bus, J.C.P. (1982). Global convergence of Newton-Like methods. In: Hennart, J.P. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092956

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  • DOI: https://doi.org/10.1007/BFb0092956

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11193-1

  • Online ISBN: 978-3-540-38986-6

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