The domain decomposition method embodies large potentials for a parallelization of FEM methods. In this data-parallel approach, the domain of interest is partitioned into smaller subdomains, either before the mesh generation or afterwards (mesh partitioning). The subdomains are assigned to processors that calculate the corresponding part of the approximation. The mesh decomposition and assignme...

A binary space partitioning (bsp) tree represents a recursive, hierarchical subdivision of d-dimensional space into convex subspaces. BSP trees provide a computational representation of space that provides both a search structure and a representation of geometry. Constructing a bsp tree consists of partitioning a subspace by means of a hyperplane, which intersects the interior of that subspace,...

Recursive partitioning algorithms separate a feature space into a set of disjoint rectangles. Then, usually, a constant in every partition is fitted. While this is a simple and intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and independent variables may look. Or it may be that a certain model is assumed or of interest and there is a nu...

Recursive partitioning is the core of several statistical methods including Classification and Regression Trees, Random Forest, and AdaBoost. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a single tree, or methods for systematically quantifying the discrepancy between two trees. Taking advantage of the recursive structure in...

This paper uses model-based recursive partitioning to study economic growth in the 255 European Union NUTS2 regions over the period 1995–2005. The starting point of the analysis is a human-capital augmented Solow-type growth equation similar in spirit to Mankiw et al. (1992). Initial GDP and the share of highly educated in the working age population are found to be important for explaining econ...

In this paper, we investigate vision-based navigation using the self-organizing hierarchical optimal subspace learning and inference framework (SHOSLIF) that incorporates states and a visual attention mechanism. With states to keep the history information and regarding the incoming video input as an observation vector, the vision-based navigation is formulated as an observation-driven Markov mo...

We present a memory efficient parallel algorithm for the solution of tridiagonal linear systems of equations that are diagonally dominant on a very large number of processors. Our algorithm can be viewed as a parallel partitioning algorithm. We illustrate its performance using some examples. Based on this partitioning algorithm, we introduce a recursive version that has logarithmic communicatio...