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On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis

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Reliable Computing

Abstract

This paper presents a new numerical algorithm based on interval analysis able to verify that a continuously differentiable function is injective. The efficiency of the method is demonstrated by illustrative examples. These examples have been treated by a C++ solver which is made available.

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Authors and Affiliations

  1. LISA, UFR Angers, 62 avenue Notre Dame du Lac, 49000, Angers, France

    Sébastien Lagrange & Nicolas Delanoue

  2. E3I2, ENSIETA, 2 rue Francois Verny, 29806, Brest Cedex 09, France

    Luc Jaulin

Authors
  1. Sébastien Lagrange
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  2. Nicolas Delanoue
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  3. Luc Jaulin
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Correspondence to Sébastien Lagrange.

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Lagrange, S., Delanoue, N. & Jaulin, L. On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis. Reliable Comput 13, 409–421 (2007). https://doi.org/10.1007/s11155-007-9042-9

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  • DOI: https://doi.org/10.1007/s11155-007-9042-9

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