Related papers: Analysis of scattered higher dimensional data usin…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…
The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order…
Predicting the evolution of spatiotemporal physical systems from sparse and scattered observational data poses a significant challenge in various scientific domains. Traditional methods rely on dense grid-structured data, limiting their…
An interpolation method to evaluate magnetic fields given unstructured, scattered magnetic data is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the…
The calculation of scattering amplitudes at higher orders in perturbation theory has reached a high degree of maturity. However, their usage to produce physical predictions within Monte Carlo programs is often precluded by the slow…
This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there…
Pulsar dynamic spectra exhibit high visibility fringes arising from interference between scattered radio waves. These fringes may be random or highly ordered patterns, depending on the nature of the scattering or refraction. Here we…
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting…
Estimating spatially distributed information through the interpolation of scattered observation datasets often overlooks the critical role of domain knowledge in understanding spatial dependencies. Additionally, the features of these data…
Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…