Open Access
2011/2012 Least Squares and Approximate Differentiation
Russell A. Gordon
Real Anal. Exchange 37(1): 189-202 (2011/2012).


The least squares derivative and the approximate derivative are both generalizations of the ordinary derivative. The existence of either of these generalized derivatives does not guarantee the existence of the other and it is even possible for both generalized derivatives to exist at a point but have different values. Several examples of such functions are presented in this paper. In addition, conditions for which the existence of the approximate derivative implies the existence (and equality) of the least squares derivative are stated and proved. These conditions involve the notion of Hölder continuity and a stronger version of approximate differentiability.


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Russell A. Gordon. "Least Squares and Approximate Differentiation." Real Anal. Exchange 37 (1) 189 - 202, 2011/2012.


Published: 2011/2012
First available in Project Euclid: 30 April 2012

zbMATH: 1247.26009
MathSciNet: MR3016859

Primary: 26A16 , 26A24
Secondary: 26A05

Keywords: approximate derivative , Hölder continuity , least squares derivative

Rights: Copyright © 2011 Michigan State University Press

Vol.37 • No. 1 • 2011/2012
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