Risk measure preserving piecewise linear approximation of empirical distributions

Piecewise Linear Orthogonal Approximation

We derive Sobolev-type inner products with respect to which hat functions on arbitrary triangulations of domains in R are orthogonal. Compared with linear interpolation, the resulting approximation schemes yield superior accuracy at little extra cost.

Edge-Preserving Piecewise Linear Image Smoothing Using Piecewise Constant Filters

Most image smoothing filters in the literature assume a piecewise constant model of smoothed output images. However, the piecewise constant model assumption can cause artifacts such as gradient reversals in applications such as image detail enhancement, HDR tone mapping, etc. In these applications, a piecewise linear model assumption is more preferred. In this paper, we propose a simple yet ver...

Piecewise Linear Approximation of Smooth Compact Fibers

Nearest piecewise linear approximation of fuzzy numbers

The problem of the nearest approximation of fuzzy numbers by piecewise linear 1-knot fuzzy numbers is discussed. By using 1-knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study. They might be also perceived as a generalization of the trapezoidal approximations. Moreover, these approximations possess some desira...

Space Efficient Approximation of Piecewise Linear Functions

In this work, we compute upper bounds of piecewise linear functions which is a special case of piecewise linear approximation. There are several application areas like pattern recognition or cartography. The goal is to reduce the number of sampling points while still preserving the characteristics of given data. The problem of approximating a given piecewise linear function with n sampling poin...