Methoden zur Bestimmung des wesentlichen Supremums mit Anwendung in der globalen Optimierung. - Aachen : Shaker, 2000. - X, 161 S.. - (Berichte aus der Mathematik) Zugl.: Ilmenau : Techn. Univ., Diss., 1999
ISBN 3826582063
On the covariance of a random sequence generated by the fractional part of multiples of a uniformly distributed random variable. - In: Stochastics and stochastics reports, ISSN 1045-1129, Bd. 66 (1999), 1/2, S. 27-35
Ein high-level Dimensionierungsverfahren für analoge Systemkomponenten am Beispiel der Modulo-Funktion. - In: Analog '99, (1999), S. 291-298
Mathematical modelling of a first order sigma-delta modulator. - In: Journal of difference equations and applications, ISSN 1563-5120, Bd. 4 (1998), 6, S. 533-550
In this paper an exact model for a basic, first order sigma-delta-modulator is derived by means of a difference equation with discontinuous nonlinearity. An explicit solution is given in terms of the greatest integer function under certain boundedness and initial conditions of the input signal. Assumptions are made under which the explicit formula remains a solution of the difference equation although the suppositions of the main theorem are violated.
http://dx.doi.org/10.1080/10236199808808161
The Hausdorff nearest circle to a convex compact set in the plane. - In: Zeitschrift für Analysis und ihre Anwendungen, ISSN 0232-2064, Bd. 17 (1998), 2, S. 479-499
The problem of finding the nearest in the Hausdorff metric circle to a non-empty convex compact set T in the plane is considered from geometrical point of view. The consideration is based on the equivalence of this problem with the Chebyshevian best approximation of 2*pi-periodic functions by trigonometric polynomials of first order, whence it follows that the Hausdorff nearest circle to a convex compact set in the plane exists and is unique. It can be characterized by a geometric Chebyshevian alternance. As a consequence in the particular case of a polygon the centre of the circle is described as an intersection of a midline between some two vertices and a bisectrix of some two sides. In the general case geometrical algorithms corresponding to the one and the four point exchange Remez algorithms are described. They assure correspondingly linear and superlinear convergence. Following the idea, in the case of a polygon to get the exact solution in finite number of steps, a modified two point exchange algorithm is suggested and illustrated by a numerical example. An application is given to estimate the Hausdorff distance between an arbitrary convex set and its Hausdorff nearest circle. The considered problem arises as a practical problem by measuring and pattern recognition in the production of circular machine parts.
Localization of multiple dipoles in bounded convex three dimensional domains by external magnetic measurements. - In: 43. Internationales Wissenschaftliches Kolloquium, (1998), insges. 6 S.
Filtering of analog digital converters using an exact time approach. - In: 43. Internationales Wissenschaftliches Kolloquium, (1998), insges. 6 S.
Parametric properties of the transportation problem and relations to supermatroids. - In: Optimization, ISSN 1029-4945, Bd. 39 (1997), 2, S. 165-189
http://dx.doi.org/10.1080/02331939708844280
Convergence speed of an integral method for computing the essential supremum. - In: Developments in global optimization, (1997), S. 153-170
We give an equivalence between the tasks of computing the essential supremum of a summable function and of finding a certain zero of a one-dimensional convex function. Interpreting the integral method as Newton-type method we show that in the case of objective functions with an essential supremum that is not spread the algorithm can work very slowly. For this reason we propose a method of accelerating the algorithm which is in some respect similar to the method of Aitken/Steffensen.
On the best approximation of set-valued functions. - In: Recent advances in optimization, (1997), S. 61-74
Let M be a Hausdorff compact topological space, let C(M) be the Banach space of the continuous on M functions supplied with the supremum norm and let V be a finite dimensional subspace of C(M). The problem of the Chebyshev approximation of a function f of C(M) by functions from V is generalized to two Chebyshev kind approximations of a point-to set mapping by a single valued continuous function from V using suitable distances between a point and a set. The first problem occur e.g. in curve fitting with noisy data or in approximating spatial bodies by circular cylinders with respect to a proper distance. The second problem is useful for calculating continuous selections with special uniform distance properties.