For interpolation of scattered multivariate data by radial basis functions, an \uncertainty relation" between the attainable error and the condition of the interpolation matrices is proven. It states that the error and the condition number cannot both be kept small. Bounds on the Lebesgue constants are obtained as a byproduct. A variation of the Narcowich{Ward theory of upper bounds on the norm...

This paper reports initial research on supporting Visually Mediated Interaction (VMI) by developing person-specific and generic gesture models for the control of active cameras. We describe a time-delay variant of the Radial Basis Function (TDRBF) network and evaluate its performance on recognising simple pointing and waving hand gestures in image sequences. Experimental results are presented t...

Multidimensional projection has become a standard tool for visual analysis of multidimensional data sets, as the 2D representation of multidimensional instances gives an important and informative panorama of the data. Recently, research in this torojection, a recently proposed resampling mechanism that allows users to generate new multidimensional instances by creating reference 2D points in th...

Moisture is one of the most important factors affecting grain quality in storage. The grain must be dried as soon as possible after harvesting to lower moisture to a standard level. It is difficult to obtain satisfactory measurement effect on precision in capacitive grain’s moisture measurement due to many influencing factors, such as temperature, species and weight. The data confusion method o...

We combine the theory of radial basis functions with the field of Galerkin methods to solve partial differential equations. After a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions.

In this chapter the use of compactly-supported radial basis functions for surface reconstruction is described. To solve the problem of reconstruction or volume data generation specially designed software is employed. Time performance of the algorithm is investigated. Thanks to the efficient octree algorithm used in this study, the resulting matrix is a band diagonal matrix that reduces computat...

A necessary condition for monitoring and control of a Power System (PS) is possessing a credible model of this system. The PS model for a need of dispatchers in national control centre is created in real time. An important element of such a model is a topology model. PS Topology Verification (PSTV) is an important problem in PS engineering. Often this problem is solved together with PS state es...

Radial basis functions are a very powerful tool in multivariate approximation since they are mesh free. In the theory of radial basis functions, the most frequently used error bounds are the one raised by Madych and Nelson in [5] and the one raised by Wu and Schaback in [6], especially the latter. It seems that Wu and Schaback’s error bound is five times more frequently used than that of Madych...

This paper, two Artificial Neural Network (ANN) models using radial basis function (RBF) nets are developed for the design of Aperture Coupled Microstrip Antennas (ACMSA) for different number of design parameters. The effect of increasing the number of design parameters on the ANN model is also discussed in this work. The performances of the models when compared are found that on decreasing the...