Sensitivity Analysis Using a Fixed Point Interval Iteration

Proving the existence of a solution to a system of real equations is a central issue in numerical analysis. In many situations, the system of equations depend on parameters which are not exactly known. It is then natural to aim proving the existence of a solution for all values of these parameters in some given domains. This is the aim of the parametrization of existence tests. A new parametric existence test based on the Hansen-Sengupta operator is presented and compared to a similar one based on the Krawczyk operator. It is used as a basis of a fixed point iteration dedicated to rigorous sensibility analysis of parametric systems of equations. Notations Vectors are denoted by boldface symbols, and interval, interval vectors and matrices by bracketed symbols. Let f : E −→ F be a function, and X ⊆ dom(f). Then f(X) := {f(x) ∈ F|x ∈ X} is the range of f on X. 1. The Hansen-Sengupta Existence Test The presentation given here follows the one given by Neumaier in [4]. The interval Gauss-Seidel is defined as follows: First in dimension one, (1) [γ] (