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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…

Numerical Analysis · Mathematics 2016-06-27 Wei Zhao , Martin Stoll

This paper proposes a distributed weighted regularized least squares algorithm (DWRLS) based on spherical radial basis functions and spherical quadrature rules to tackle spherical data that are stored across numerous local servers and…

Machine Learning · Computer Science 2022-11-15 Han Feng , Shao-Bo Lin , Ding-Xuan Zhou

Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data.…

Numerical Analysis · Mathematics 2025-05-23 Amirhossein Fashamiha , David Salac

We mainly concerned with a decoupled fractional Laplacian wave equation in this paper. A new time-space domain radial basis function (RBF) collocation method is introduced to solve the fractional wave equation, which describes seismic wave…

Computational Physics · Physics 2018-06-07 Yiran Xu , Jingye Li , Guofei Pang , Zhikai Wang , Xiaohong Chen , Benfeng Wang

Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…

In this work, we propose an adaptive radial basis function (RBF) approach for the efficient solution of multidimensional spatiotemporal integrodifferential equations. Our approach can automatically adjust the shape of RBFs and provide an…

Numerical Analysis · Mathematics 2026-04-08 Mingtao Xia , Qijing Shen

Multiphysics simulations frequently require transferring solution fields between subproblems with non-matching spatial discretizations, typically using interpolation techniques. Standard methods are usually based on measuring the closeness…

Numerical Analysis · Mathematics 2024-03-07 Michele Bucelli , Francesco Regazzoni , Luca Dede' , Alfio Quarteroni

When solving partial differential equations on scattered nodes using the Radial Basis Function-generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs…

Numerical Analysis · Mathematics 2026-02-26 Andrej Kolar-Požun , Mitja Jančič , Miha Rot , Gregor Kosec

In this paper we present an effective coarse space correction addressed to accelerate the solution of an algebraic linear system. The system arises from the formulation of the problem of interpolating scattered data by means of Radial Basis…

Numerical Analysis · Mathematics 2019-12-10 Guillaume Gbikpi-Benissan , Frederic Magoules

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

Numerical Analysis · Mathematics 2023-09-07 Zhiwen Wang , Minxin Chen , Jingrun Chen

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…

Numerical Analysis · Mathematics 2007-05-23 F. Lanzara , V. Maz'ya , G. Schmidt

In this paper, we discuss the problem of constructing Radial Basis In this paper, we discuss the problem of constructing Radial Basis Function (RBF)-based Partition of Unity (PU) interpolants that are positive if data values are positive.…

Numerical Analysis · Mathematics 2017-01-26 Alessandra De Rossi , Emma Perracchione

We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF…

Machine Learning · Statistics 2021-01-12 Sam Davanloo Tajbakhsh , Necdet Serhat Aybat , Enrique del Castillo

In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…

Computation · Statistics 2024-09-17 Antony Sikorski , Daniel McKenzie , Douglas Nychka

Global radial basis function (RBF) collocation methods with inifinitely smooth basis functions for partial differential equations (PDEs) work in general geometries, and can have exponential convergence properties for smooth solution…

Numerical Analysis · Mathematics 2020-01-31 Elisabeth Larsson , Ulrika Sundin

In this paper, we address the problem of predicting complex, nonlinear spatiotemporal dynamics when available data is recorded at irregularly-spaced sparse spatial locations. Most of the existing deep learning models for modeling…

Machine Learning · Computer Science 2022-07-13 Priyabrata Saha , Saibal Mukhopadhyay

Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address…

Machine Learning · Statistics 2021-05-05 Ruoxi Wang , Yingzhou Li , Michael W. Mahoney , Eric Darve

This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…

Numerical Analysis · Mathematics 2024-12-20 Víctor Bayona , Argyrios Petras , Cécile Piret , Steven J. Ruuth

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…

Numerical Analysis · Mathematics 2017-04-27 Yong-Xia Hao , Chong-Jun Li , Ren-Hong Wang

Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…

Computation · Statistics 2020-02-18 Andrew Zammit-Mangion , Jonathan Rougier