Numerische Mathematik

, Volume 27, Issue 4, pp 485–490 | Cite as

Backward error analysis for totally positive linear systems

  • Carl de Boor
  • Allan Pinkus
Article
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Summary

Gauss elimination applied to ann×n matrixA in floating point arithmetic produces (if successful) a factorization\(\hat L\hat U\) which differs fromA by no more than\(\gamma |\hat L|{\text{ }}|\hat U|\), for some γ of ordern times the unit roundoff. IfA is totally positive, then both computed factors\(\hat L\) and\(\hat U\) are nonnegative for sufficiently small unit roundoff and one obtains pleasantly small bounds for the perturbation inA which would account for the rounding errors committed in solvingAx=b forx by Gauss eliminationwithout pivoting. It follows that the banded linear system for the B-spline coefficients of an interpolating spline function can be solved safely by Gauss elimination without pivoting.

Keywords

Linear System Mathematical Method Error Analysis Small Unit Spline Function 
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 1977

Authors and Affiliations

  • Carl de Boor
    • 1
  • Allan Pinkus
    • 1
  1. 1.Mathematics Research CenterUniversity of WisconsinMadisonUSA

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