Data point selection for piecewise linear curve approximation

Improving Piecewise-linear Approximation by Relaxing on End Point Constraint

We consider the problem of approximating a polygonal curve P with n vertices by a sequence Q of m line segments, where m ≤ n−1. The goal is to minimize the error between P and Q under certain metric. Previously the problem was solved by constraining the line segments of Q to be sequentially connected and their end points be from P . In this paper we remove the end point constraint to achieve a ...

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.

Bilinear amplitude approximation for piecewise-linear oscillators

Currently, the interest in monitoring the vibration of dynamical systems has been increasing. For example, large and complex air and space structures include vibration monitoring systems to forecast sudden failures. Such vibration monitoring is used to diagnose structural health by analyzing vibration characteristics (such as frequency and amplitude). Among the vibration characteristics used, t...

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...