Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
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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.

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DOI: https://doi.org/10.1090/qam/78045
Article copyright: © Copyright 1956 American Mathematical Society

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