Algorithm 666. CHABIS: A mathematical software package for locating and evaluating roots of systems of nonlinear equations CHABIS is a mathematical software package for the numerical solution of a system of n nonlinear equations in n variables. First, CHABIS locates at least one solution of the system within an n-dimensional polyhedron. Then, it applies a new generalized method of bisection to this n-polyhedron in order to obtain an approximate solution of the system according to a predetermined accuracy. In this paper we briefly describe the user interface to CHABIS and present several details of its implementation, as well as an example of its usage

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 16 articles )

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  1. Vrahatis, M.N.; Tsirogiannis, G.A.; Laskari, E.C.: Novel orbit based symmetric cryptosystems (2010)
  2. Malihoutsaki, E.N.; Nikas, I.A.; Grapsa, T.N.: Improved Newton’s method without direct function evaluations (2009)
  3. Tanabé, S.; Vrahatis, M.N.: On perturbation of roots of homogeneous algebraic systems (2006)
  4. Kavvadias, D.J.; Makri, F.S.; Vrahatis, M.N.: Efficiently computing many roots of a function (2005)
  5. Vrahatis, M.N.; Magoulas, G.D.; Plagianakos, V.P.: From linear to nonlinear iterative methods (2003)
  6. Mourrain, B.; Vrahatis, M.N.; Yakoubsohn, J.C.: On the complexity of isolating real roots and computing with certainty the topological degree (2002)
  7. Boutsinas, B.; Vrahatis, M.N.: Artificial nonmonotonic neural networks (2001)
  8. Kravanja, P.; Verlinden, P.: On the zeros of $J_n(z)\pm iJ_n+1(z)$ and $[J_n+1(z)]^2- J_n(z) J_n+2(z)$ (2001)
  9. Plagianakos, V.P.; Nousis, N.K.; Vrahatis, M.N.: Locating and computing in parallel all the simple roots of special functions using PVM (2001)
  10. Grapsa, T.N.; Vrahatis, M.N.: A dimension-reducing method for unconstrained optimization (1996)
  11. Vrahatis, Michael N.; Triantafyllou, Evangelia C.: Locating, characterizing and computing the stationary points of a function (1996)
  12. Vrahatis, M.N.; Bountis, T.C.: Periodic orbits and invariant surfaces of nonlinear mappings (1996)
  13. Vrahatis, Michael N.: An efficient method for locating and computing periodic orbits of nonlinear mappings (1995)
  14. Vrahatis, M.N.; Ragos, O.; Skiniotis, T.; Zafiropoulos, F.A.; Grapsa, T.N.: RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions (1995)
  15. Greene, John M.: Locating three-dimensional roots by a bisection method (1992)
  16. Vrahatis, Michael N.: Algorithm 666. CHABIS: A mathematical software package for locating and evaluating roots of systems of nonlinear equations (1988)