Open Access
2009/2010 A Least Squares Approach to Differentiation
Russell A. Gordon
Real Anal. Exchange 35(1): 205-228 (2009/2010).


We consider an approach to differentiation that involves least squares lines of best fit rather than the traditional secant lines and use elementary techniques to show how this leads to the Lanczos derivative. A number of examples are presented to illustrate this concept and to show that the product, quotient, and chain rules fail for the Lanczos derivative. Several results giving conditions for which these rules do hold are discussed and proved. A brief introduction to higher order Lanczos derivatives is included.


Download Citation

Russell A. Gordon. "A Least Squares Approach to Differentiation." Real Anal. Exchange 35 (1) 205 - 228, 2009/2010.


Published: 2009/2010
First available in Project Euclid: 27 April 2010

zbMATH: 1124.26004
MathSciNet: MR2657296

Primary: 26A16 , 26A24

Keywords: H\"older continuity , Lanczos derivative , Peano derivative

Rights: Copyright © 2009 Michigan State University Press

Vol.35 • No. 1 • 2009/2010
Back to Top