Determining the locations and discontinuities in the derivatives of functions

Rick Archibald; Anne Gelb; Jungho Yoon

doi:10.1016/j.apnum.2007.01.018

Determining the locations and discontinuities in the derivatives of functions

Rick Archibald, Anne Gelb, Jungho Yoon

Data Analysis and Machine Learning

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

We introduce a method for detecting discontinuities in piecewise smooth functions and in their derivatives. The method is constructed from a local stencil of grid point values and is based on a polynomial annihilation technique. By varying the order of the method and the arrangement of the corresponding stencils, the jump discontinuities of a function and its derivatives can be identified with high order accuracy. The method is efficient and robust and can be applied to non-uniform distributions in one dimension.

Original language	English
Pages (from-to)	577-592
Number of pages	16
Journal	Applied Numerical Mathematics
Volume	58
Issue number	5
DOIs	https://doi.org/10.1016/j.apnum.2007.01.018
State	Published - May 2008

Funding

Anne Gelb has been supported in part by NSF grants CNS 0324957, DMS 0510813, DMS 0608844, and NIH No. EB 025533-01. Jungho Yoon has been supported by the grant Seoul Research and Business Development Program 10646. Rick Archibald has been supported by the Householder Fellowship in Scientific Computing sponsored by the DOE Applied Mathematical Sciences program. Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC for the US Department of Energy under Contract No. DE-AC05-00OR22725. Oak Ridge National Lab, PO Box 2008, MS6367, Oak Ridge, TN 37831-6367.

Keywords

Derivative discontinuities
Edge detection
Piecewise smooth functions
Polynomial annihilation

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10.1016/j.apnum.2007.01.018

Cite this

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Determining the locations and discontinuities in the derivatives of functions

Abstract

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Keywords

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