Minimal and maximal real roots of parametric polynomials using interval analysis In this paper we are interested in parametric polynomials, i.e. polynomials whose coefficients are analytical functions of parameters that are restricted to lie within given ranges. We propose algorithms based on interval analysis to solve various problems such as finding the extremal real roots for the set of polynomials and determining an approximation of the set of parameters values such that all the polynomials have their root real part in a given range. Realistic application examples are presented in the field of robotics and control theory.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Goulianas, K.; Margaris, A.; Refanidis, I.; Diamantaras, K.: An adaptive learning rate backpropagation-type neural network for solving (n\timesn) systems on nonlinear algebraic equations (2016)
  2. Neveu, Bertrand; Trombettoni, Gilles; Araya, Ignacio: Adaptive constructive interval disjunction: algorithms and experiments (2015)
  3. Silva, Ricardo M. A.; Resende, Mauricio G. C.; Pardalos, Panos M.: Finding multiple roots of a box-constrained system of nonlinear equations with a biased random-key genetic algorithm (2014)
  4. Araya, Ignacio; Neveu, Bertrand; Trombettoni, Gilles: An interval extension based on occurrence grouping (2012)
  5. Sielemann, M.; Schmitz, G.: A quantitative metric for robustness of nonlinear algebraic equation solvers (2011)
  6. Domes, Ferenc; Neumaier, Arnold: Constraint propagation on quadratic constraints (2010)
  7. Tsoulos, I. G.; Stavrakoudis, Athanassios: On locating all roots of systems of nonlinear equations inside bounded domain using global optimization methods (2010)
  8. Hirsch, Michael J.; Pardalos, Panos M.; Resende, Mauricio G. C.: Solving systems of nonlinear equations with continuous GRASP (2009)
  9. Toutounian, F.; Saberi-Nadjafi, J.; Taheri, S. H.: A hybrid of the Newton-GMRES and electromagnetic meta-heuristic methods for solving systems of nonlinear equations (2009)
  10. Goualard, Frédéric; Jermann, Christophe: A reinforcement learning approach to interval constraint propagation (2008)
  11. Ben Horin, P.; Djerassi, S.; Shoham, M.; Ben Horin, R.: Dynamics of a six degrees-of-freedom parallel robot actuated by three two-wheel carts (2006)
  12. Merlet, J.-P.: Parallel robots. (2006)
  13. Neumaier, Arnold; Shcherbina, Oleg; Huyer, Waltraud; Vinkó, Tamás: A comparison of complete global optimization solvers (2005)
  14. The COPRIN Project: Minimal and maximal real roots of parametric polynomials using interval analysis (2003)