A LEAST SQUARES APPROACH TO DIFFERENTIATION

被引：0
|
作者：
Gordon, Russell A. [1 ]
机构：
[1] Whitman Coll, Dept Math, Walla Walla, WA 99362 USA
来源：
REAL ANALYSIS EXCHANGE | 2009年 / 35卷 / 01期
关键词：
Lanczos derivative; Holder continuity; Peano derivative;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：205 / 228
页数：24
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