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On the choice of initial guesses for the Newton-Raphson algorithm

Author

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  • Casella, Francesco
  • Bachmann, Bernhard

Abstract

The initialization of equation-based differential-algebraic system models, and more in general the solution of many engineering and scientific problems, require the solution of systems of nonlinear equations. Newton-Raphson’s method is widely used for this purpose; it is very efficient in the computation of the solution if the initial guess is close enough to it, but it can fail otherwise. In this paper, several criteria are introduced to analyze the influence of the initial guess on the evolution of Newton-Raphson’s algorithm and to identify which initial guesses need to be improved in case of convergence failure. In particular, indicators based on first and second derivatives of the residual function are introduced, whose values allow to assess how much the initial guess of each variable can be responsible for the convergence failure. The use of such criteria, which are based on rigorously proven results, is successfully demonstrated in three exemplary test cases.

Suggested Citation

  • Casella, Francesco & Bachmann, Bernhard, 2021. "On the choice of initial guesses for the Newton-Raphson algorithm," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    • Handle: RePEc:eee:apmaco:v:398:y:2021:i:c:s0096300321000394
    DOI: 10.1016/j.amc.2021.125991
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    References listed on IDEAS

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    1. Carpanzano, Emanuele & Maffezzoni, Claudio, 1998. "Symbolic manipulation techniques for model simplification in object-oriented modelling of large scale continuous systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(2), pages 133-150.
    2. Emanuele Carpanzano, 2000. "Order Reduction of General Nonlinear DAE Systems by Automatic Tearing," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 6(2), pages 145-168, June.
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