Bisection method in higher dimensions and the efficiency number

Dániel Bachrathy, Gábor Stépán

Research output: Contribution to journalArticle

46 Citations (Scopus)


Several engineering applications need a robust method to find all the roots of a set of nonlinear equations automatically. The proposed method guarantees monotonous convergence, and it can determine whole submanifolds of the roots if the number of unknowns is larger than the number of equations. The critical steps of the multidimensional bisection method are described and possible solutions are proposed. An efficient computational scheme is introduced. The efficiency of the method is characterized by the box-counting fractal dimension of the evaluated points. The multidimensional bisection method is much more efficient than the brute force method. The proposed method can also be used to determine the fractal dimension of the submanifold of the solutions with satisfactory accuracy.

Original languageEnglish
Pages (from-to)81-86
Number of pages6
JournalPeriodica Polytechnica Mechanical Engineering
Issue number2
Publication statusPublished - 2012



  • Bisection method
  • Efficiency number
  • Multi dimension
  • Multiple roots
  • System of non-linear equations

ASJC Scopus subject areas

  • Mechanical Engineering

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