Epsilon-inflation in verification algorithms

Epsilon-inflation in verification algorithms Epsilon-inflation is often used in verification numerics to find an interval vector ( x ) ∈ such that some interval function (ƒ) maps ( x ) ∈ into itself. We recall algorithms which use epsilon-inflation to verify this subset property (ƒ) ((x) ϵ ) ⊆ (x) ϵ , and we derive criteria which guarantee that already finitely many inflation steps are sufficient to prove it. These criteria require (ƒ) to be a P-contraction. We recall results on P-contractions, and we derive rules to verify them. We also introduce local P-contractions, and we use this concept to guarantee again the subset property above when using epsilon-inflation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational and Applied Mathematics Elsevier

Epsilon-inflation in verification algorithms

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Publisher
Elsevier
Copyright
Copyright © 1995 Elsevier Ltd
ISSN
0377-0427
eISSN
1879-1778
DOI
10.1016/0377-0427(94)00089-J
Publisher site
See Article on Publisher Site

Abstract

Epsilon-inflation is often used in verification numerics to find an interval vector ( x ) ∈ such that some interval function (ƒ) maps ( x ) ∈ into itself. We recall algorithms which use epsilon-inflation to verify this subset property (ƒ) ((x) ϵ ) ⊆ (x) ϵ , and we derive criteria which guarantee that already finitely many inflation steps are sufficient to prove it. These criteria require (ƒ) to be a P-contraction. We recall results on P-contractions, and we derive rules to verify them. We also introduce local P-contractions, and we use this concept to guarantee again the subset property above when using epsilon-inflation.

Journal

Journal of Computational and Applied MathematicsElsevier

Published: Jun 20, 1995

References

  • Matrix Iterative Analysis
    Varga, R.S.

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