Nicolas Delanoue

Using interval arithmetic to prove that a set is path-connected

In this paper, we give a numerical algorithm able to prove whether a set S described by nonlinear inequalities is path-connected or not. To our knowledge, no other algorithm (numerical or symbolic) is able to deal with this type of problem. The proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected components as S. Examples illustrate the principle of the approach.

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

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.

Guaranteeing the Homotopy Type of a Set Defined by Non-Linear Inequalities

This paper provides an effective method to create an abstract simplicial complex homotopy equivalent to a given set

Counting the number of connected components of a set and its application to robotics

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Guaranteed SLAM—An interval approach

described by non-linear inequalities (polynomial or not). To our knowledge, no other numerical algorithm is able to deal with this type of problem. The proposed approach divides

Technical communique: Injectivity analysis using interval analysis: Application to structural identifiability

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