A statistical approach for economization of the polynomial functions

Abstract

Due to having the minimax property, Chebyshev polynomials are used today to economize the arbitrary polynomial functions. In this work, we present a statistical approach to show that, contrary to current thought, the Chebyshev polynomials of the first kind are not appropriate for economizing these polynomials if one uses this statistical approach. In this way, a numerical results section is also given to clearly prove our claim.

Keywords:

• Polynomial function economization
• First and second kind Chebyshev polynomials
• Polynomial approximation
• Probability value

Acknowledgements

The authors would like to thank the referee for carefully reading the paper.