Univariate adaptive thinning

Authors:
Nira Dyn;Michael S. Floater;Armin Iske
Affiliations:
Tel Aviv Univ., Tel Aviv, Israel;SINTEF, Oslo, Norway;Technische Univ. München, Munich, Germany
Venue:
Mathematical Methods for Curves and Surfaces
Year:
2001

Citing 2
Cited 3

Algorithms

Algorithms
Multistep scattered data interpolation using compactly supported radial basis functions

Journal of Computational and Applied Mathematics - Special issue on scattered data

Adaptive thinning for bivariate scattered data

Journal of Computational and Applied Mathematics
Progressive scattered data filtering

Journal of Computational and Applied Mathematics
Enhancement of spatially adaptive smoothing splines via parameterization of smoothing parameters

Computational Statistics & Data Analysis

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Abstract

In this paper we approximate large sets of univariate data by piecewise linear functions which interpolate subsets of the data, using adaptive thinning strategies. Rather than minimize the global error at each removal (AT0), we propose a much cheaper thinning strategy (AT1) which only minimizes errors locally. Interestingly, the two strategies are equivalent in all our numerical tests and we prove this to be true for convex data. We also compare with non-adaptive thinning strategies.