As scientiic technology becomes increasingly more sophisticated, the production of more data and/or the modelling of more complex systems requires computers with ever-increasing computational power. In order to cope with this situation numerical algorithms have to be developed which allow the distribution of both data and code segments over large numbers of processors with the hope that problem...

We consider certain systems of linear operator equations where the n-th order solution is made unique by an initial value taken from the preceeding solution. Such conditions arise in the enumeration of lattice paths with weighted left turns, if the paths are restricted by a lower linear barrier of integer slope. 1 Introduction All our lattice paths take unit steps in the " North (= y) and ! Eas...

In this paper, fuzzy initial value problems for modelling aspects of uncertainty in dynam­ ical systems are introduced and interpreted from a probabilistic point ofview. Due to the uncertainty incorporated in the model, the behavior of dynamical systems modelIed in this way will generally not be unique. Rather, we obtain a large set of trajectories which are more or less compatible with the des...

h.0/ D 0; h.t/ D g t; h.t/ ; t 2 Œ0; 1 (1) in h W Œ0; 1 ! R (Figure 1). A simple sufficient condition that guarantees unique existence of solution h is that g be Lipschitz continuous (along its second argument), which is to say, jg.t;y0/ g.t;y1/j L jy0 y1j; t 2 Œ0; 1; y0;y1 2 R (2) for some constant L independent of y0, y1 and t [16]. We are interested in the computational complexity of the ...