A fast segmentation algorithm for piecewise polynomial numeric function generators
TL;DR: An efficient algorithm for partitioning the domain of a numeric function f into segments is given and an estimate of segment width based on local derivatives greatly reduces the search needed to determine the exact segment width.
read more
About: This article is published in Journal of Computational and Applied Mathematics. The article was published on 01 May 2011. and is currently open access. The article focuses on the topics: Piecewise & Polynomial.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
On the number of segments needed in a piecewise linear approximation
TL;DR: This work shows that, if the segments have the same width (to reduce circuit complexity), then the number of segments is given by s(@e)~c@e, (@e->0^+), where c=(b-a)|f^''|"m"a"x4.
48
Optimal Polygonal $L_{1}$ Linearization and Fast Interpolation of Nonlinear Systems
TL;DR: In this paper, a principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L 1 norm.
Diode piecewise-linear function approximation circuit with current input and output
David Kubanek
- 13 Oct 2011
TL;DR: The paper describes the design of a piecewise-linear function approximation generator operating in current mode based on a resistive current divider whose gain is controlled by switching diodes.
3
Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation
TL;DR: This paper proposes a novel hierarchical MILP formulation and fast iterative algorithm to approximate non-linear functions with piecewise linear functions, achieving minimum segments and error, and demonstrates its efficiency in tightening and warm-starting the MILP problem for large data sets.
3
Efficient Table-based Function Approximation on FPGAs using Interval Splitting and BRAM Instantiation
TL;DR: Three interval-splitting algorithms are proposed to reduce the required memory footprint drastically based on the observation that in sub-intervals of low gradient, a coarser sampling grid may be assumed to satisfy the maximum interpolation error bound.
References
Algorithms for the reduction of the number of points required to represent a digitized line or its caricature
TL;DR: In this paper, two algorithms to reduce the number of points required to represent the line and, if desired, produce caricatures are presented and compared with the most promising methods so far suggested.
4.3K
•Book
Elementary Functions: Algorithms and Implementation
Jean-Michel Muller
- 15 Jul 1997
TL;DR: I found the book well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find.
676
Approximating elementary functions with symmetric bipartite tables
TL;DR: In this paper, a high-speed method for function approximation that employs symmetric bipartite tables is presented, which uses less memory by taking advantage of symmetry and leading zeros in one of the two tables.
181
•Book
Numerical methods for computer science, engineering, and mathematics
John H. Mathews
- 01 Jan 1987
TL;DR: The Numerical Methods for Computer Science, Engineering, and Mathematics (NML) as mentioned in this paper is a popular method for numerical methods for computer science, engineering, and mathematics applications.
180
MATLAB Programming for Engineers
Stephen Lynch
- 01 Jan 2011
TL;DR: One of the many ventures in the UK National Higher Education Science, Technology, Engineering and Mathematics (HE STEM) programme is the Supporting MATLAB Automated assessment to Reinforce Teaching (SMART) project as mentioned in this paper.
162