A gradient descent method for solving a system of nonlinear equations

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Abstract

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.

Original languageEnglish (US)
Article number106739
JournalApplied Mathematics Letters
Volume112
DOIs
StatePublished - Feb 2021

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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