This paper establishes a direct method for solving variational problems via a set of Radial basis functions (RBFs) with Gauss-Chebyshev collocation centers. The method consist of reducing a variational problem into a mathematical programming problem. The authors use some optimization techniques to solve the reduced problem. Accuracy and stability of the multiquadric, Gaussian and inverse multiq...

The importance of graph search algorithm choice to the directed relation graph with error propagation (DRGEP) method is studied by comparing basic and modified depth-first search, basic and R-value-based breadth-first search (RBFS), and Dijkstra’s algorithm. By using each algorithm with DRGEP to produce skeletal mechanisms from a detailed mechanism for nheptane with randomly-shuffled species or...

Where distributed agents must share voluminous set membership information, Bloom filters provide a compact, though lossy, way for them to do so. Numerous recent networking papers have examined the trade-offs between the bandwidth consumed by the transmission of Bloom filters, and the error rate, which takes the form of false positives, and which rises the more the filters are compressed. In thi...

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are ‘flat’ leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vec...

We describe a Fourier Volume Rendering (FVR) algorithm for datasets that are irregularly sampled and require anisotropic (e.g., elliptical) kernels for reconstruction. We sample the continuous frequency spectrum of such datasets by computing the continuous Fourier transform of the spatial interpolation kernel which is a radially symmetric basis function (RBF) that may be anisotropically scaled....

This paper describes a method for surface reconstruction from sparse three-dimensional (3D) data that performs the reconstruction by building a sequence of surfaces approximating the data at increasing level of details (LOD). The method is simple, fast and suitable for a progressive 3D data/model representation, archiving, transmission. The surface reconstruction is obtained by a volumetric met...

We present a novel hierarchical spatial partitioning method for creating interpolating implicit surfaces using compactly supported radial basis functions (RBFs) from scattered surface data. From this hierarchy of functions we can create a range of models from coarse to fine, where a coarse model approximates and a fine model interpolates. Furthermore, our method elegantly handles irregularly sa...

Several analytical and numerical methods exist to solve the orbit propagation of the two-body problem. Analytic solutions are mainly implemented for the unperturbed/classical two-body problem. Numerical methods can handle both the unperturbed and the perturbed two-body problem. The literature is rich with numerical methods addressing orbit propagation problems such as, Gauss-Jackson, Higher ord...

In this study we aim to define a mapping function that relates the general index value among a set of shares to the prices of individual shares. In more general terms this is problem of defining the relationship between multivariate data distributions and a specific source of variation within these distributions where the source of variation in question represents a quantity of interest related...