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A parametric Kantorovich theorem with application to tolerance synthesis

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Abstract

We propose a parametric Kantorovich theorem, which will achieve these two tasks. The idea is to compute worst case Kantorovich constants with respect to parameters q using a branch and bound algorithm dedicated to nonlinear nonsmooth global optimization. A rigorous first order model of the dependence with respect to parameters p is used to enforce the convergence of the error upper-bound. Details about these developments can be found in [1]. We provide here a different point of view, in particular emphasizing the reason why not using the interval Newton operator, in spite of its theoretical superiority on Kantorovich theorem in this context [2].
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Dates and versions

hal-01863731 , version 1 (29-08-2018)

Identifiers

  • HAL Id : hal-01863731 , version 1

Cite

Alexandre Goldsztejn, Stéphane Caro, Gilles Chabert. A parametric Kantorovich theorem with application to tolerance synthesis. The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations, Sep 2018, Tokyo, Japan. ⟨hal-01863731⟩
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