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Optimal Piecewise Polynomial Approximation for Minimum Computing Cost by Using Constrained Least Squares
Version 1
: Received: 30 May 2024 / Approved: 30 May 2024 / Online: 30 May 2024 (15:51:18 CEST)
A peer-reviewed article of this Preprint also exists.
Song, J.; Lee, B. Optimal Piecewise Polynomial Approximation for Minimum Computing Cost by Using Constrained Least Squares. Sensors 2024, 24, 3991. Song, J.; Lee, B. Optimal Piecewise Polynomial Approximation for Minimum Computing Cost by Using Constrained Least Squares. Sensors 2024, 24, 3991.
Abstract
In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares. In time-sensitive applications or in embedded systems with limited resources, the runtime of the approximate function is as crucial as its accuracy. The proposed algorithm search to find the Optimal Piecewise Polynomial (OPP) with minimum computational cost while ensuring the error below a specified threshold. This was accomplished by using smooth piecewise polynomials with optimal order and number of intervals. The computational cost only depends on polynomial complexity, i.e., the order and the number of intervals at runtime function call. For optimal approximation, computational costs for all the possible combinations of piecewise polynomials were calculated and tabulated as ascending order for the specific target CPU off-line. Each combination was optimized through constrained least squares and random selection method for given sample points. Afterward, whether the approximation error is below the predetermined value is examined. When the error is permissible, the combination is selected as the optimal approximation or the next combination was examined. To verify the performance, several representative functions were examined and analyzed.
Keywords
piecewise polynomial, function-approximation, regression, constrained least squares
Subject
Engineering, Electrical and Electronic Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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