A note on numerical differentiation
Author:
John W. Miles
Journal:
Quart. Appl. Math. 14 (1956), 97-101
MSC:
Primary 65.0X
DOI:
https://doi.org/10.1090/qam/78045
MathSciNet review:
78045
Full-text PDF Free Access
Abstract |
Similar Articles |
Additional Information
Abstract: Given the matrix $f = \{{f_i}\}$, representing $f\left ( x \right )$ at the set of points $\{ {x_i}\}$, the $m$th derivatives of $f\left ( x \right )$ at these points are expressed in terms of all of the ${f_i}$ according to ${f^{\left ( m \right )}} = {C^{ - 1}}{A^m}Cf$, where A is the sum of the skew matrix $\left [ {{{\left ( {{x_i} - {x_i}} \right )}^{ - 1}}} \right ]$ and the diagonal matrix formed by summing the terms in the corresponding rows of this skew matrix, and C is the diagonal matrix having as its elements the products of the elements in the corresponding rows of the skew matrix.
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
65.0X
Retrieve articles in all journals
with MSC:
65.0X
Additional Information
Article copyright:
© Copyright 1956
American Mathematical Society