Rounding Error Analysis of Elementary Numerical Algorithms

  • F. Stummel
Part of the Computing Supplementum book series (COMPUTING, volume 2)


The paper presents a new rounding error analysis of product and summation algorithms, Horner’s scheme, evaluations of finite continued fractions, computations of determinants of tridiagonal systems, of determinants of second order and a ’fast’ complex multiplication. The error analysis uses the linearization method and new condition numbers constituting optimal bounds in appraisals of the possible errors. The new error estimates are tested by numerous numerical examples.


Condition Number Error Equation Arithmetic Operation Partial Product Floating Point 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • F. Stummel
    • 1
  1. 1.Fachbereich MathematikJohann-Wolfgang-Goethe-UniversitätFrankfurt am MainFederal Republic of Germany

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