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.
Description
A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting - Springer
%0 Journal Article
%1 noKey
%A Deuflhard, P.
%D 1974
%I Springer-Verlag
%J Numerische Mathematik
%K 1974 algorithm mathematics root-finding
%N 4
%P 289-315
%R 10.1007/BF01406969
%T A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting
%U http://dx.doi.org/10.1007/BF01406969
%V 22
%X 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.
@article{noKey,
abstract = {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.},
added-at = {2014-01-15T18:56:01.000+0100},
author = {Deuflhard, P.},
biburl = {https://www.bibsonomy.org/bibtex/225133f1fc3669845a735226c47b3f0a0/thorade},
description = {A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting - Springer},
doi = {10.1007/BF01406969},
interhash = {bb5ec7991d393468eed8b344a87ee85b},
intrahash = {25133f1fc3669845a735226c47b3f0a0},
issn = {0029-599X},
journal = {Numerische Mathematik},
keywords = {1974 algorithm mathematics root-finding},
language = {English},
number = 4,
pages = {289-315},
publisher = {Springer-Verlag},
timestamp = {2014-01-15T18:56:01.000+0100},
title = {A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting},
url = {http://dx.doi.org/10.1007/BF01406969},
volume = 22,
year = 1974
}