%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 }