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Numerical Stability Properties

  • Phillip RegaliaEmail author
  • Richard Le Borne
Chapter

Abstract

Designers of algorithms must not only solve the problem of interest, but do so using methods which are robust under perturbations in the data as well as the intermediate parameters of the method. More generally, it is often the case that the actual problem of interest is too complicated to solve directly; simplifying assumptions are necessary. At each stage, from problem identification, to the setup of the problem to be solved using some method, to the ultimate algorithm to be implemented in code, perturbations and their effects must be anticipated and analyzed. Stability is the property that assesses the level of robustness to perturbations that is required before the computed solution given by an algorithm can be used with confidence. The origin of the perturbation can vary, as pointed out above. What is important, however, is to have analysis that supports the premise that a small change in the problem results in a small change to the solution.

Keywords

Compute Solution Cholesky Factor Reachable State Triangular Array Roundoff Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Catholic University of AmericaWashingtonUSA
  2. 2.Tennessee Technological UniversityCookevilleUSA

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