BIT Numerical Mathematics

, Volume 45, Issue 4, pp 653–677 | Cite as

Monotonicity Preserving Approximation of Multivariate Scattered Data

  • G. Beliakov


This paper describes a new method of monotone interpolation and smoothing of multivariate scattered data. It is based on the assumption that the function to be approximated is Lipschitz continuous. The method provides the optimal approximation in the worst case scenario and tight error bounds. Smoothing of noisy data subject to monotonicity constraints is converted into a quadratic programming problem. Estimation of the unknown Lipschitz constant from the data by sample splitting and cross-validation is described. Extension of the method for locally Lipschitz functions is presented.

Key words

monotone approximation isotone approximation scattered data central algorithm optimal approximation 


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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.School of Information TechnologyDeakin UniversityBurwoodAustralia

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