an:07281300
Zbl 1454.65033
Hao, Wenrui
A gradient descent method for solving a system of nonlinear equations
EN
Appl. Math. Lett. 112, Article ID 106739, 9 p. (2021).
0893-9659
2021
j
65H10 90C53
gradient descent method; systems of nonlinear equations; convergence analysis
Summary: This paper develops a gradient descent (GD) method for solving a system of nonlinear equations with an explicit formulation. We theoretically prove that the GD method has linear convergence in general and, under certain conditions, is equivalent to Newton's method locally with quadratic convergence. A stochastic version of the gradient descent is also proposed for solving large-scale systems of nonlinear equations. Finally, several benchmark numerical examples are used to demonstrate the feasibility and efficiency compared to Newton's method.