On the interval hull of solution sets of parametrised nonlinear equations

The paper considers bounding sets of solutions to parametrised nonlinear equations with coefficients subject to uncertainties. Of particular interest is the set theoretic co-multiplication of two intervals expressed in the form mid point-radius intervals. An improvement of formulae of higher order for disk inversion as afforded by Carstensen and Petkovic (1994) is employed to facilitate our computation using the interval LU decomposition method as well as interval Gauss-Siedel iterative method. The big gain is that interval method has capability of removing the dependency problem if the values of the uncertainties are not large owing to the enclosures of inner estimations. It is shown that large uncertainties imply large nonlinearities and this may drastically affect the performance of all methods based on centered forms.