Zuzana Majdisova

Zuzana Majdisova, Vaclav Skala

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher dimension d>2, because the other methods require the conversion of a scattered dataset to an ordered dataset (i.e. a semi-regular mesh is obtained by using some tessellation techniques), which is computationally expensive. The RBF approximation is non-separable, as it is based on the distance between two points. This method leads to a solution of Linear System of Equations (LSE) Ac=h. In this paper several RBF approximation methods are briefly introduced and a comparison of those is made with respect to the stability and accuracy of computation. The proposed RBF approximation offers lower memory requirements and better quality of approximation.

Zuzana Majdisova, Vaclav Skala

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is based on a distance between two points. This method leads to a solution of overdetermined linear system of equations. In this paper a new approach to the RBF approximation of large datasets is introduced and experimental results for different real datasets and different RBFs are presented with respect to the accuracy of computation. The proposed approach uses symmetry of matrix and partitioning matrix into blocks.

Zuzana Majdisova, Vaclav Skala, Michal Smolik

Stationary points of multivariable function which represents some surface have an important role in many application such as computer vision, chemical physics, etc. Nevertheless, the dataset describing the surface for which a sampling function is not known is often given. Therefore, it is necessary to propose an approach for finding the stationary points without knowledge of the sampling function. In this paper, an algorithm for determining a set of stationary points of given sampled surface and detecting the bindings between these stationary points (such as stationary points lie on line segment, circle, etc.) is presented. Our approach is based on the piecewise RBF interpolation of the given dataset.