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
BUS, J.C.P. [1980], Numerical solution of systems of nonlinear equations, Mathematical Centre Tracts 122, Amsterdam.
DENNIS Jr., J.E. & J.J. MORÉ [1977], Quasi-Newton methods, motivation and theory, SIAM Rev. 19, 46–89.
DEUFLHARD, P., [1974a], A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting, Numer. Math. 22, 289–315.
DEUFLHARD, P. [1974b], A relaxation strategy for the modified Newton method in: Conference on optimization and optimal control, BULIRSCH, R., W. OETTLI & J. STOER (eds), Oberwolfach, Springer, Berlin.
DEUFLHARD, P. & G. HEINDL [1979], Affine invariant convergence theorems for Newton's method and extensions to related methods, SIAM J. Numer. Anal. 16, 1–10.
KANTOROVICH, L.W. & G. P. AKILOW [1964], Functional analysis in normed spaces (german), publ. by P.H. Müller, transl. from Russ. by H. Langer and R. Kühne, Berlin, Akademie-Verlag, Math. Lehrbücher und Monographien: 2.17.
ORTEGA, J. M. & W.C. RHEINBOLDT [1970], Iterative solution of nonlinear equations in several variables, Academic Press, New York & London.
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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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