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2006/2007 Orthogonal Polynomials and Regression-Based Symmetric Derivatives
Nathanial Burch, Paul E. Fishback
Real Anal. Exchange 32(2): 597-608 (2006/2007).


We demonstrate how certain types of symmetric derivatives originate from a simple least-squares regression problem involving discrete Chebyshev polynomials. As the number of data points used in this regression tends to infinity, the resulting integrals, which involve Legendre polynomials, lead to Lanczos derivatives, a result that demonstrates how this latter entity is merely a continuous version of the symmetric derivative.


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Nathanial Burch. Paul E. Fishback. "Orthogonal Polynomials and Regression-Based Symmetric Derivatives." Real Anal. Exchange 32 (2) 597 - 608, 2006/2007.


Published: 2006/2007
First available in Project Euclid: 3 January 2008

zbMATH: 1131.26002
MathSciNet: MR2369869

Primary: 26A24
Secondary: 33C45 , 62J02

Keywords: discrete Chebyshev and Legendre polynomials , regression , symmetric and Lanczos derivatives

Rights: Copyright © 2006 Michigan State University Press

Vol.32 • No. 2 • 2006/2007
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