220 research outputs found
Endoscopic surgery of an extensive aneurysmatic bone cyst of the paranasal sinuses in a 12-year-old patient
Computational Complexity of Iterated Maps on the Interval (Extended Abstract)
The exact computation of orbits of discrete dynamical systems on the interval
is considered. Therefore, a multiple-precision floating point approach based on
error analysis is chosen and a general algorithm is presented. The correctness
of the algorithm is shown and the computational complexity is analyzed. As a
main result, the computational complexity measure considered here is related to
the Ljapunow exponent of the dynamical system under consideration
Verified global optimization for estimating the parameters of nonlinear models
Nonlinear parameter estimation is usually achieved via the minimization of some possibly non-convex cost function. Interval analysis allows one to derive algorithms for the guaranteed characterization of the set of all global minimizers of such a cost function when an explicit expression for the output of the model is available or when this output is obtained via the numerical solution of a set of ordinary differential equations. However, cost functions involved in parameter estimation are usually challenging for interval techniques, if only because of multi-occurrences of the parameters in the formal expression of the cost. This paper addresses parameter estimation via the verified global optimization of quadratic cost functions. It introduces tools for the minimization of generic cost functions. When an explicit expression of the output of the parametric model is available, significant improvements may be obtained by a new box exclusion test and by careful manipulations of the quadratic cost function. When the model is described by ODEs, some of the techniques available in the previous case may still be employed, provided that sensitivity functions of the model output with respect to the parameters are available
On the selection of subdivision directions in interval branch-and-bound methods for global optimization
Presentation of a highly tuned multithreaded interval solver for underdetermined and well-determined nonlinear systems
The theoretical and empirical rate of convergence for geometric branch-and-bound methods
Decomposition of Minkowski–Rådström–Hörmander Space to the Direct Sum of Symmetric and Asymmetric Subspaces
- …