The method of determining all real nonmultiple roots of systems of nonlinear equations Export

@article{citeulike:4836728, abstract = {A method for determining all nonmultiple roots of the system of nonlinear equations in an n-dimensional parallelepiped is proposed. The main idea of the method is that the original set, in which the roots are sought, is divided into subsets where either the system of equations does not have solutions or its Jacobian matrix is nonsingular. A partition algorithm is presented and its convergence is proved. The application of the method is demonstrated using several examples.}, author = {Semenov, V.}, citeulike-article-id = {4836728}, citeulike-linkout-0 = {http://dx.doi.org/10.1134/S0965542507090047}, citeulike-linkout-1 = {http://www.springerlink.com/content/yu503754v1645lq5}, day = {29}, doi = {10.1134/S0965542507090047}, journal = {Computational Mathematics and Mathematical Physics}, keywords = {equations, jacobian, localization, matrix, method, newton, nonlinear, of, root, system, zeros}, month = {September}, number = {9}, pages = {1428--1434}, posted-at = {2009-06-13 17:15:44}, priority = {0}, title = {The method of determining all real nonmultiple roots of systems of nonlinear equations}, url = {http://dx.doi.org/10.1134/S0965542507090047}, volume = {47}, year = {2007} }

TY - JOUR ID - citeulike:4836728 L3 - citeulike-article-id:4836728 N2 - A method for determining all nonmultiple roots of the system of nonlinear equations in an n-dimensional parallelepiped is proposed. The main idea of the method is that the original set, in which the roots are sought, is divided into subsets where either the system of equations does not have solutions or its Jacobian matrix is nonsingular. A partition algorithm is presented and its convergence is proved. The application of the method is demonstrated using several examples. IS - 9 JF - Computational Mathematics and Mathematical Physics EP - 1434 TI - The method of determining all real nonmultiple roots of systems of nonlinear equations VL - 47 SP - 1428 KW - equations KW - jacobian KW - localization KW - matrix KW - method KW - newton KW - nonlinear KW - of KW - root KW - system KW - zeros AU - Semenov, V PY - 2007/09/29/ UR - http://dx.doi.org/10.1134/S0965542507090047 ER -