Related papers: Numerical cubature on scattered data by adaptive i…
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…
We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…
Bayesian cubature (BC) is a popular inferential perspective on the cubature of expensive integrands, wherein the integrand is emulated using a stochastic process model. Several approaches have been put forward to encode sequential…
Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…
The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…
In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on…
Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…
In this paper, we deal with the challenging computational issue of interpolating large data sets, with eventually non-homogeneous densities. To such scope, the Radial Basis Function Partition of Unity (RBF-PU) method has been proved to be a…
We use asymptotically optimal \emph{adaptive} numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot…
Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing…
This study investigates the computational speed and accuracy of two numerical integration methods, cubature and sampling-based, for integrating an integrand over a 2D polygon. Using a group of rovers searching the Martian surface with a…
The quality of datasets is a critical issue in big data mining. More interesting things could be mined from datasets with higher quality. The existence of missing values in geographical data would worsen the quality of big datasets. To…
In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs)…
Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate…
We describe an algorithm for controlling the relative error in the numerical evaluation of a bivariate integral, without prior knowledge of the magnitude of the integral. In the event that the magnitude of the integral is less than unity,…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
Many applications require multi-dimensional numerical integration, often in the form of a cubature formula. These cubature formulas are desired to be positive and exact for certain finite-dimensional function spaces (and weight functions).…
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…
In this contribution we introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. We focus the attention on the ellipse, an annulus and a polygon. An upper bound for such an operator is…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…