Determining the locations and discontinuities in the derivatives of functions

Rick Archibald, Anne Gelb, Jungho Yoon

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


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 languageEnglish (US)
Pages (from-to)577-592
Number of pages16
JournalApplied Numerical Mathematics
Issue number5
StatePublished - May 2008


  • Derivative discontinuities
  • Edge detection
  • Piecewise smooth functions
  • Polynomial annihilation

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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