Numerical Algorithms

, Volume 78, Issue 2, pp 625–641 | Cite as

Always convergent methods for nonlinear equations of several variables

  • A. Galántai
Original Paper


We develop always convergent methods for solving nonlinear equations of the form \(f\left (x\right ) =0\) (\(f:\mathbb {R}^{n}\rightarrow \mathbb {R}^{m}\), \(x\in B=\times _{i=1}^{n}\left [ a_{i},b_{i}\right ] \)) under the assumption that f is continuous on B. The suggested methods use continuous space curves lying in the rectangle B and have a kind of monotone convergence to the nearest zero on the given curve, if it exists, or the iterations leave the region in a finite number of steps. The selection of space curves is also investigated. The numerical test results indicate the feasibility and limitations of the suggested methods.


Nonlinear equations Continuous functions Global convergence Space filling curves 

Mathematics Subject Classification (2010)

65H10 65H05 65H20 47H10 


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The author is indebted to the unknown referee whose remarks and suggestions improved the paper.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Óbuda UniversityBudapestHungary

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