A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence nea...A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton＇s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.展开更多
We obtain the double factorization of braided bialgebras or braided Hopf algebras and give the relations among integrals and semisimplicity of braided Hopf algebra and its factors.
基金Foundation item： Supported by the National Science Foundation of China（10701066）
文摘A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton＇s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.
基金the Foundation of Hunan University (No.521101365)
文摘We obtain the double factorization of braided bialgebras or braided Hopf algebras and give the relations among integrals and semisimplicity of braided Hopf algebra and its factors.
