Efficient Piecewise-Linear Function Approximation Using the Uniform Metric (1994)
| Venue: | Discrete & Computational Geometry |
| Citations: | 33 - 0 self |
BibTeX
@ARTICLE{Goodrich94efficientpiecewise-linear,
author = {Michael T. Goodrich},
title = {Efficient Piecewise-Linear Function Approximation Using the Uniform Metric},
journal = {Discrete & Computational Geometry},
year = {1994},
volume = {14},
pages = {322--331}
}
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Abstract
We give an O(n log n)-time method for finding a best k-link piecewise-linear function approximating an n-point planar data set using the well-known uniform metric to measure the error, ffl 0, of the approximation. Our method is based upon new characterizations of such functions, which we exploit to design an efficient algorithm using a plane sweep in "ffl space" followed by several applications of the parametric searching technique. The previous best running time for this problem was O(n 2 ). 1 Introduction Approximating a set S = f(x 1 ; y 1 ); (x 2 ; y 2 ); : : : ; (x n ; y n )g of points in the plane by a function is a classic problem in applied mathematics. The general goals in this area of research are to find a function F belonging to a class of functions F such that each F 2 F is simple to describe, represent, and compute and such that the chosen F approximates S well. For example, one may desire that F be the class of linear or piecewise-linear functions, and, for any parti...
