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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.

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|December 9, 2021
PubMed
Summary
This summary is machine-generated.

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.

Keywords:
Algorithm testingapproximationcomputational experimentleast absolute deviationpolynomial approximationtest problems

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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.