Piecewise linear approximation
Authors: Tianhong Tan, Shoudong Zhu (CHEME 6800, 2021 Fall)
Introduction
Currently, approximating a complex non-linear function or smooth curve is very common in industry area. Like the very popular one, piecewise linear approximation, which is applied in a variety of real-world areas, such as signal processing and image processing in electronics information industry, pattern recognition in AI area[1]. The problem of piecewise linear approximation can be classified by which type of norms applied in approximating process, whether the length of segments is fixed or not and whether the approximation is continuity or discontinuity[2]. We can use piecewise linear approximation to represent any non-linear or linear function by any accuracy order by any accuracy by adding more nodes or segments until the accuracy is met[3]. The meaning of piecewise linear approximation's existence is it allow us to transform non-linear problem to be solved by linear formation, which is easier to be executed by machine and the amount of calculation is acceptable[4].
Theory, Methodology & Algorithms
Numerical Example
Applications
Conclusion
References
- ↑ G. Manis, G. Papakonstantinou and P. Tsanakas, "Optimal piecewise linear approximation of digitized curves," Proceedings of 13th International Conference on Digital Signal Processing, 1997, pp. 1079-1081 vol.2, doi: 10.1109/ICDSP.1997.628552.