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.
The original publication can be found at www.springerlink.com
Field of Research
080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective
970108 Expanding Knowledge in the Information and Computing Sciences
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