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Generators for Discrete Polynomial L1 Approximation Problems
P Domich1, J Lawrence1, D Shier1
1Center for Applied Mathematics, National Bureau of Standards, Washington, DC 20234.
New software tools automatically generate polynomial approximation problems for testing curve-fitting algorithms. These generators create problems with specific features and known solutions, aiding in the evaluation of discrete L1 approximation codes.
Area of Science:
- Numerical Analysis
- Computational Mathematics
- Computer Science
Background:
- Polynomial approximation is crucial for empirical curve-fitting.
- Existing methods for generating test problems may lack flexibility.
- Discrete L1 approximation is a key technique in data analysis.
Purpose of the Study:
- To develop and implement novel generators for polynomial approximation problems.
- To facilitate the testing and validation of discrete L1 approximation codes.
- To enable the creation of problems with controllable characteristics and known solutions.
Main Methods:
- Development of two distinct algorithms for problem generation.
- Implementation of these generators in a software framework.
- Utilizing the generators to create diverse test cases for L1 approximation.
Main Results:
- Successful creation of two functional problem generators.
- Demonstrated ability to generate problems with specified characteristics.
- One generator provides known, unique, and controllable solutions.
Conclusions:
- The developed generators are effective tools for creating polynomial approximation problems.
- These tools enhance the rigorous testing of discrete L1 approximation algorithms.
- Future work can leverage these generators for broader algorithm development and analysis.
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