Skip to main content
Log in

A rapid Generalized Method of Bisection for solving Systems of Non-linear Equations

  • About Cubature Formulas with a Minimal Number of Knots
  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary

A rapid Generalized Method of Bisection for solving Systems of Non-linear Equations is presented in this paper, based on the non-zero value of the topological degree. Further, while the method does not compute the topological degree, it takes care of keeping its non-zero value during the bisections and thus results in a fast bisection algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alexandroff, P., Hopf, H.: Topologie. Berlin, Heidelberg, New York: Springer 1935; reprinted: New York: Chelsea 1965

    Google Scholar 

  2. Cronin, J.: Fixed points and topological degree in nonlinar analysis. Am. Math. Soc. Surv.11 (1964)

  3. Keartfott, R.B.: Computing the degree of maps and a generalized method of bisection. Ph. D. disseration, University of Utah, S.L.C. 1977

  4. Kearfott, R.B.: An efficient degree-computation method for a generalized method of bisection. Numer. Math.32, 109–127 (1979)

    Google Scholar 

  5. Ortega, S.M., Rheinboldt, W.C.: Iterative solution of nonlinear equations in several variables. New York: Academic Press 1970

    Google Scholar 

  6. Stenger, F.: Computing the topological, degree of a mapping in ℝn. Numer. Math.25, 23–38 (1975)

    Google Scholar 

  7. Stynes, M.: On the construction of sufficient refinements for computation of topological degree. Number. Math.37, 453–462 (1981)

    Google Scholar 

  8. Vrahatis, M.N.: The topological degree for the generalized method of bisection. Technical Report 6, Department of Mathematics, University of Patras, Patras, Greece 1981

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vrahatis, M.N., Iordanidis, K.I. A rapid Generalized Method of Bisection for solving Systems of Non-linear Equations. Numer. Math. 49, 123–138 (1986). https://doi.org/10.1007/BF01389620

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01389620

Subject Classifications

Navigation