On the choice of initial guesses for the Newton-Raphson algorithm
作者：
Highlights：
• Only the initial guesses of variables affecting the Jacobian of a nonlinear system of equations influence the convergence of Newton’s method.
• Sufficient conditions for the reduction of the residuals after the first iteration of Newton’s method are given.
• Numerical indicators are defined to highlight which initial guesses of Newton’s method are farthest from the solution.
• Criteria based on those indicators are given to identify which initial guesses should be corrected in case of convergence failure of Newton’s method
• The criteria require the computation of the Jacobians and Hessians of the nonlinear equation residuals and are applicable to any system of equations.
摘要
•Only the initial guesses of variables affecting the Jacobian of a nonlinear system of equations influence the convergence of Newton’s method.•Sufficient conditions for the reduction of the residuals after the first iteration of Newton’s method are given.•Numerical indicators are defined to highlight which initial guesses of Newton’s method are farthest from the solution.•Criteria based on those indicators are given to identify which initial guesses should be corrected in case of convergence failure of Newton’s method•The criteria require the computation of the Jacobians and Hessians of the nonlinear equation residuals and are applicable to any system of equations.
论文关键词：Newton-Raphson’s algorithm,Convergence,Nonlinear equations,Equation-based modelling
论文评审过程：Received 19 December 2019, Revised 6 October 2020, Accepted 5 January 2021, Available online 27 January 2021, Version of Record 27 January 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.125991
