Algorithm 681: INTBIS, a portable interval Newton/bisection package. We present a portable software package for finding all real roots of a system of nonlinear equations within a region defined by bounds on the variables. Where practical, the package should find all roots with mathematical certainty. Though based on interval Newton methods, it is self-contained. It allows various control and output options and does not require programming if the equations are polynomials; it is structured for further algorithmic research. Its practicality does not depend in a simple way on the dimension of the system or on the degree of nonlinearity. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 31 articles , 1 standard article )

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  1. Araya, Ignacio; Neveu, Bertrand: \textttlsmear: a variable selection strategy for interval branch and bound solvers (2018)
  2. Henderson, Nélio; Rêgo, Marroni de Sá; Imbiriba, Janaína: Topographical global initialization for finding all solutions of nonlinear systems with constraints (2017)
  3. Araya, Ignacio; Reyes, Victor: Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects (2016)
  4. Neveu, Bertrand; Trombettoni, Gilles; Araya, Ignacio: Node selection strategies in interval branch and bound algorithms (2016)
  5. Alexandre dit Sandretto, Julien; Trombettoni, Gilles; Daney, David: Interval methods for model qualification: methodology and advanced application (2014)
  6. Just, Elke: Subdivision strategies for boxes in branch-and-bound nonlinear solvers and verification (2014)
  7. 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)
  8. Andrei, Neculai: Nonlinear optimization applications using the GAMS technology (2013)
  9. Stradi-Granados, Benito A.: Interval arithmetic for nonlinear problem solving (2013)
  10. Ishii, Daisuke; Goldsztejn, Alexandre; Jermann, Christophe: Interval-based projection method for under-constrained numerical systems (2012)
  11. Stuber, M. D.; Kumar, V.; Barton, P. I.: Nonsmooth exclusion test for finding all solutions of nonlinear equations (2010)
  12. Merlet, Jean-Pierre: Interval analysis for certified numerical solution of problems in robotics (2009)
  13. Pedamallu, Chandra Sekhar; Ozdamar, Linet; Ceberio, Martine: Efficient interval partitioning-local search collaboration for constraint satisfaction (2008)
  14. Kearfott, R. Baker; Neher, Markus; Oishi, Shin’ichi; Rico, Fabien: Libraries, tools, and interactive systems for verified computations four case studies (2004)
  15. Mourrain, B.; Vrahatis, M. N.; Yakoubsohn, J. C.: On the complexity of isolating real roots and computing with certainty the topological degree (2002)
  16. Merlet, J.-P.: A parser for the interval evaluation of analytical functions and its application to engineering problems (2001)
  17. Graham, R. L.; Lubachevsky, B. D.; Nurmela, Kari J.; Östergård, Patric R. J.: Dense packings of congruent circles in a circle (1998)
  18. Hardin, R. H.; Sloane, N. J. A.: McLaren’s improved snub cube and other new spherical designs in three dimensions (1996)
  19. Balaji, Gopalan V.; Seader, J. D.: Application of interval Newton’s method to chemical engineering problems (1995)
  20. Hu, Chenyi; Sheldon, Joe; Kearfott, R. Baker; Yang, Qing: Optimizing INTBIS on the CRAY Y-MP (1995)

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