Minisymposium on Applications of Interval
Computations at the Third World Congress of
Catania, Sicily, Italy, July 19–26, 2000
On July 19–26, 2000 the third World Congress of Nonlinear Analysts was held
in Catania, Sicily, Italy. This huge conference with over 1350 talks attracted
researchers from all over the world. On July 21, a minisymposium on the applica-
tions of interval computations took place.
In the ﬁrst talk, Ken Jackson gave a short introduction to interval computations
and surveyed validated methods for the numerical solution of initial value prob-
lems for ordinary differential equations, focusing on interval Hermite-Obreshkov
methods and on a method by which the wrapping effect is considerably reduced.
Martin Berz studied the motion of objects in the solar system and particle
trajectories in accelerator rings. His method uses the approach of Taylor models
which permits the control of the so-called dependency problem as well as the
wrapping effect. The method was applied to the study of possible collision of near-
earth asteroids with earth within an advanced relativistic NASA model of the solar
Siegfried Rump presented a new method for ﬁnding an approximation and
inclusion of multiple eigenvalues of matrices. His results are of special interest, as
up to now only inclusions for simple and double eigenvalues are known.
Eric Walter discussed three applications of interval analysis to the estimation of
the parameter or state vector of a model from experimental data, viz. ﬁnding all pos-
sible positions of a Stewart-Gough platform from the lengths of its limbs, compart-
mental modelling, and robust autonomous localization of a static and mobile robot.
In all three cases, there were several radically different and equally valid solutions,
and interval techniques were instrumental in ﬁnding accurate outer approximations
for all of them.
ı applied modal interval analysis, e.g. to predictive control systems,
and presented an interval based digital controller which improves the dynamic
performance of parametrically uncertain systems.
urgen Garloff explained the use of the expansion of a multivariate polynomial
into Bernstein polynomials for ﬁnding bounds for the range of such a polynomial
over a box and applied this expansion to computing an enclosure for the solution