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Chebyshev model arithmetic for factorable functions.

Jai Rajyaguru1, Mario E Villanueva1, Boris Houska2

  • 11Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ UK.

Journal of Global Optimization : an International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering
|February 15, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces Chebyshev models for approximating factorable functions, offering tighter bounds than Taylor models but with increased computational cost. The research details their convergence properties and arithmetic operations.

Keywords:
Chebyshev modelsConvergence rateFactorable functionsGlobal optimizationInterval analysisTaylor models

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Area of Science:

  • Numerical Analysis
  • Computer Science

Background:

  • Taylor models are used for function approximation.
  • Chebyshev models offer an alternative with potential for tighter bounds.

Purpose of the Study:

  • To present an arithmetic for Chebyshev models.
  • To analyze their convergence properties for factorable functions.

Main Methods:

  • Developing propagation rules for arithmetic operations (addition, multiplication, composition).
  • Establishing local and global convergence bounds.
  • Implementing Chebyshev model arithmetic in the MC++ library.

Main Results:

  • Chebyshev models provide tighter interval bounds compared to Taylor models.
  • The arithmetic operations and convergence properties were analyzed.
  • Numerical case studies demonstrated the trade-off between bound tightness and computational cost.

Conclusions:

  • Chebyshev models offer a valuable tool for function approximation with improved accuracy.
  • The computational overhead is a key consideration when choosing between Chebyshev and Taylor models.