Stefan Siegmund

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We establish a new class of three-point methods for the computation of simple zeros of a scalar function. Based on the two-point optimal method by Ostrowski (1966), we construct a family of order eight methods which use three evaluations of f and one of f′ and therefore have an efficiency index equal to 8 4 ≈ 1 . 682 $\sqrt [4]{8}\approx 1.682$ and are(More)
We deal with dynamic equations on time scales, where we characterize the positivity of a system. Uniform exponential stability of a system is determined by the spectrum of its matrix. We investigate the corresponding stability radii with respect to structured perturbations and show that for positive systems the complex stability radius and the positive(More)
The method of invariant manifolds was originally developed for hyperbolic rest points of autonomous equations. It was then extended from fixed points to arbitrary solutions and from autonomous equations to nonautonomous dynamical systems by either the Lyapunov–Perron approach or Hadamard’s graph transformation. We go one step further and study meaningful(More)
In networked control systems, the Try-Once-Discard (TOD) protocol is of high interest because its properties can be characterized by Lyapunov functions. This feature makes it practical to incorporate TOD into Lyapunov-based design of linear and nonlinear control systems, yielding a self-contained theory for system stabilization. In previous work, candidates(More)
Bone remodeling is regulated by pathways controlling the interplay of osteoblasts and osteoclasts. In this work, we apply the method of generalized modeling to systematically analyse a large class of models of bone remodeling. Our analysis shows that osteoblast precursors can play an important role in the regulation of bone remodeling. Further, we find that(More)
We study a family of rational maps acting on the Riemann sphere with a single preperiodic critical orbit. Using a generalization of the well-known Sierpinski gasket, we provide a complete topological description of their Julia sets. In addition, we present a combinatorial algorithm that allows us to show when two such Julia sets are not topologically(More)