%0 Journal Article %1 Frontini2004771 %A Frontini, M. %A Sormani, E. %D 2004 %J Applied Mathematics and Computation %K 2004 algorithm mathematics root-finding %N 3 %P 771 - 782 %R 10.1016/S0096-3003(03)00178-4 %T Third-order methods from quadrature formulae for solving systems of nonlinear equations %U http://dx.doi.org/10.1016/S0096-3003(03)00178-4 %V 149 %X We extend to p-dimensional problems a modification of the Newton method, based on quadrature formulas of order at least one, which produces iterative methods with order of convergence three. A general error analysis providing the higher order of convergence is given. These new methods may be more efficient then other third-order methods as they do not require the use of the second-order Fréchet derivative.

@article{Frontini2004771, abstract = {We extend to p-dimensional problems a modification of the Newton method, based on quadrature formulas of order at least one, which produces iterative methods with order of convergence three. A general error analysis providing the higher order of convergence is given. These new methods may be more efficient then other third-order methods as they do not require the use of the second-order Fréchet derivative.}, added-at = {2013-01-06T21:21:14.000+0100}, author = {Frontini, M. and Sormani, E.}, biburl = {https://www.bibsonomy.org/bibtex/23a648e54b42a0aea8d83bc56757dc57b/thorade}, description = {ScienceDirect.com - Applied Mathematics and Computation - Third-order methods from quadrature formulae for solving systems of nonlinear equations}, doi = {10.1016/S0096-3003(03)00178-4}, interhash = {7d8c07973f4661027df337716a2979ef}, intrahash = {3a648e54b42a0aea8d83bc56757dc57b}, issn = {0096-3003}, journal = {Applied Mathematics and Computation}, keywords = {2004 algorithm mathematics root-finding}, number = 3, pages = {771 - 782}, timestamp = {2013-01-06T21:21:14.000+0100}, title = {Third-order methods from quadrature formulae for solving systems of nonlinear equations}, url = {http://dx.doi.org/10.1016/S0096-3003(03)00178-4}, volume = 149, year = 2004 }