Sensitivity Analysis Using a Fixed Point Interval Iteration
This work addresses the problem of rigorous sensitivity analysis for parametric systems of equations, which is important in numerical analysis, but the contribution appears incremental as it extends an existing operator to a parametric setting without demonstrating clear advantages.
The paper introduces a new parametric existence test based on the Hansen-Sengupta operator for proving the existence of solutions to parametric systems of equations, and uses it as a basis for a fixed point iteration for rigorous sensitivity analysis. The method is compared to a similar test based on the Krawczyk operator, but no concrete numerical results are provided.
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.