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Backward Errors and Condition Numbers of Regular and Singular Points on Algebraic Curves

  • Joab R. Winkler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)

Abstract

Expressions for the componentwise and normwise backward errors at an arbitrary point on an algebraic curve are derived and the formulae that relate them to the condition numbers are established. The expressions for the condition numbers at a regular point that is near a singular point are examined and it is shown that restrictions on their validity arise in this circumstance. In particular, the lowest order approximation that is used when condition numbers are derived places tight bounds on the maximum allowable perturbation on this class of point. An example that illustrates this limitation is given.

Keywords

Singular Point Condition Number Normal Component Unit Normal Vector Regular Point 
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References

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    Walker, R.J.: Algebraic Curves. Dover, New York (1978)zbMATHGoogle Scholar
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    Winkler, J.R.: Condition numbers of a nearly singular simple root of a polynomial. Applied Numerical Mathematics 38, 275–285 (2001)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Joab R. Winkler
    • 1
  1. 1.Sheffield UniversitySheffieldUnited Kingdom

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