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A gradient descent method for solving a system of nonlinear equations. (English) Zbl 1454.65033
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.
65H10 Numerical computation of solutions to systems of equations
90C53 Methods of quasi-Newton type
Bertini; Adam; KELLEY
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