TY - JOUR
T1 - Modified Newton-NDSS Method for Solving Nonlinear System with Complex Symmetric Jacobian Matrices
AU - Yu , Xiaohui
AU - Wu , Qingbiao
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 295
EP - 314
PY - 2024
DA - 2024/04
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1012
UR - https://global-sci.org/intro/article_detail/ijnam/23028.html
KW - Modified Newton-NDSS method, complex nonlinear systems, Hölder continuous condition, symmetric Jacobian matrix, convergence analysis.
AB - <p style="text-align: justify;">An efficient iteration method is provided in this paper for solving a class of nonlinear systems whose Jacobian matrices are complex and symmetric. The modified Newton-NDSS
method is developed and applied to the class of nonlinear systems by adopting the modified
Newton method as the outer solver and a new double-step splitting (NDSS) iteration scheme as
the inner solver. Additionally, we theoretically analyze the local convergent properties of the new
method under the weaker Hölder conditions. Lastly, the new method is compared numerically with
some existing ones and the numerical experiments solving the nonlinear equations demonstrate
the superiority of the Newton-NDSS method.</p>