Approximating a Function with a Jump Discontinuity—The High-Noise Case
Abstract
:1. Introduction
2. Our Approach
2.1. The Model
2.2. Training Data
2.3. Approximating the Function from Its Samples
3. Numerical Results
3.1. Detecting the Interval of the Discontinuity and Approximating the Function
3.2. Comparing Our Approach with Two Other Approaches
3.3. Error Measurement of Approximations of Functions
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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0.30 | 0.60 | 0.90 | 1.20 | 1.50 | 1.80 | 2.10 | 2.40 | |
0.00 | 0.38 | 0.47 | 0.50 | 0.49 | 0.48 | 0.49 | 0.48 | 0.49 |
0.10 | 0.10 | 0.28 | 0.45 | 0.50 | 0.50 | 0.53 | 0.48 | 0.51 |
0.20 | 0.10 | 0.21 | 0.29 | 0.42 | 0.46 | 0.46 | 0.50 | |
0.30 | 0.12 | 0.14 | 0.24 | 0.29 | 0.37 | 0.42 | ||
0.40 | 0.11 | 0.14 | 0.19 | 0.25 | 0.31 | |||
0.50 | 0.11 | 0.13 | 0.17 | 0.22 | ||||
0.60 | 0.11 | 0.13 | 0.17 | |||||
0.70 | 0.10 | 0.12 | ||||||
0.80 | 0.12 |
0.30 | 0.60 | 0.90 | 1.20 | 1.50 | 1.80 | 2.10 | 2.40 | |
0.00 | 0.24 | 0.24 | 0.28 | 0.24 | 0.26 | 0.25 | 0.24 | 0.23 |
0.10 | 0.30 | 0.27 | 0.25 | 0.25 | 0.27 | 0.24 | 0.25 | 0.27 |
0.20 | 0.30 | 0.26 | 0.28 | 0.24 | 0.25 | 0.28 | 0.25 | |
0.30 | 0.33 | 0.28 | 0.29 | 0.26 | 0.28 | 0.28 | ||
0.40 | 0.34 | 0.30 | 0.30 | 0.26 | 0.30 | |||
0.50 | 0.34 | 0.32 | 0.30 | 0.28 | ||||
0.60 | 0.32 | 0.29 | 0.33 | |||||
0.70 | 0.34 | 0.31 | ||||||
0.80 | 0.33 |
0.30 | 0.60 | 0.90 | 1.20 | 1.50 | 1.80 | 2.10 | 2.40 | |
0.00 | 0.89 | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
0.10 | 0.53 | 0.93 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
0.20 | 0.67 | 0.92 | 0.98 | 1.00 | 1.00 | 1.00 | 1.00 | |
0.30 | 0.73 | 0.92 | 0.97 | 0.99 | 1.00 | 1.00 | ||
0.40 | 0.76 | 0.90 | 0.95 | 0.98 | 0.99 | |||
0.50 | 0.79 | 0.89 | 0.94 | 0.97 | ||||
0.60 | 0.79 | 0.88 | 0.95 | |||||
0.70 | 0.79 | 0.88 | ||||||
0.80 | 0.79 |
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Muzaffar, Q.; Levin, D.; Werman, M. Approximating a Function with a Jump Discontinuity—The High-Noise Case. AppliedMath 2024, 4, 561-569. https://doi.org/10.3390/appliedmath4020030
Muzaffar Q, Levin D, Werman M. Approximating a Function with a Jump Discontinuity—The High-Noise Case. AppliedMath. 2024; 4(2):561-569. https://doi.org/10.3390/appliedmath4020030
Chicago/Turabian StyleMuzaffar, Qusay, David Levin, and Michael Werman. 2024. "Approximating a Function with a Jump Discontinuity—The High-Noise Case" AppliedMath 4, no. 2: 561-569. https://doi.org/10.3390/appliedmath4020030