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A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting

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Numerische Mathematik, 22 (4): 289-315 (1974)
DOI: 10.1007/BF01406969

Аннотация

In this paper the well-known modified (underrelaxed, damped) Newton method is extended in such a way as to apply to the solution of ill-conditioned systems of nonlinear equations, i.e. systems having a “nearly singular” Jacobian at some iterate. A special technique also derived herein may be useful, if only bad initial guesses of the solution point are available. Difficulties that arose previously in the numerical solution of nonlinear two-point boundary value problems by multiple shooting techniques can be removed by means of the results presented below.

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