Ole Caprani

Mean value forms in interval analysis

An interval extension of a function written in the centered form or the mean value form offers a second order approximation to the range of values of the function over an interval. However, the two forms differ with respect to inclusion monotonicity; the mean value form is inclusion monotone while the centered form is not. This is demonstrated in the following paper. Further, the mean value form is more generally applicable, and a mean value form for an integral operator is considered. It is shown that this form is also a second order inclusion monotone approximation.ZusammenfassungSowohl in der zentrierten Form wie auch in der Mittelwertform liefert die Intervall-Fortsetzung einer Funktion eine Näherung zweiter Ordnung für den Wertebereich der Funktion über einem Intervall. Die beiden Formen unterscheiden sich jedoch bezüglich der Einschließungsmonotonie: Die Mittelwertform ist einschließungsmonoton, die zentrierte Form dagegen i.a. nicht, wie in der Arbeit gezeigt wird. Ferner ist die Mittelwertform allgemeiner anwendbar; eine Mittelwertform für einen Integraloperator wird diskutiert, und es wird gezeigt, daß sie ebenfalls eine einschließungsmonotone Näherung zweiter Ordnung ist.

Iterative methods for interval inclusion of fixed points

The paper discusses a technique for handling numerical, iterative processes that combines the efficiency of ordinary floating-point iterations with the accuracy control that may be obtained by iterations in interval arithmetic. As illustration the technique is used for the solution of fixed point problems in one and several variables.

SHAM, a method for biexpone ial carve resolution using initial slope, height, area and moment of the experimental decay type curve

Abstract A method for biexponesitial fitting of decay type curves is described. Basically the four unknowns are calculated from four curve parameters, viz. the initial slope (S), the initial height (H), the area (A) and the first time moment (M) with extrapolation to infinity being accomplished algebraically. The SHAM algorithm was considerably faster than a conventional iterative regression analysis (Gauss) and the results of the two methods were quite comparable both in synthetic and real data. The latter stemmed from 133xenon wash-out studies of regional blood flow in the human brain. Fast analysis of such data was the primary aim of developing the new method.

Integration of Interval Functions

An interval function Y assigns an interval

Roundoff errors in floating-point summation

Y(x) = (y(x),\bar y(x)]

Contraction mappings in interval analysis

in the extended real number system to each x in its interval

Implementation of a low round-off summation method

X = [a,b]

Existence Test for Asynchronous Interval Iteration

of definition. The integral of Y over

INTERVAL CONTRACTIONS FOR THE SOLUTION OF INTEGRAL EQUATIONS

[a,b]

Robot-Supported Food Experiences

is taken to be the interval