A low cost and highly accurate technique for big data spatial-temporal interpolation
type: Item
instance of: scholarly article
title: A low cost and highly accurate technique for big data spatial-temporal interpolation
zbMATH Open document ID: 1444.65007
author: O. Chatrabgoun
author: A. Hosseinian-Far
author: R. Montasari
author: A. Daneshkhah
author: M. Esmaeilbeigi
published in: Applied Numerical Mathematics
publication date: 2020-04-07T00:00:00Z
full work available at URL: Esmaeilbeigi Mohsen etal Elsevier 2020 A Low Cost and Highly Accurate Technique for Big Data Spatial Temporal Interpolation.pdf
review text: Multivariate approximation and interpolation, for instance with radial basis functions, is a fruitful approach to the handling of big data. In contrast to approximation by polynomials or even piecewise polynomials -- splines -- the radial basis function approach usually provides higher accuracy, more stability and low computational cost. It is in particular available for scattered data in any dimension, too. On top of this, any number of data can be dealt with, so this is an excellent approach to big data. In this article, the computational efficiency is improved further by computing the approximations to big data with a layered algorithm, where at each layer, a relatively small linear system of equations must be solved in order to compute the approximation. The well-known and very useful multiquadrics radial basis function \(\phi(r)=\sqrt{r^2+c^2}\) with the radius \(r\) and a parameter \(c\) is employed as the (radial basis) kernel function. As a numerical example the air pollution in the US is studied computationally.
Mathematics Subject Classification ID: 65D12
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 7188159
zbMATH Keywords: spatial-temporal interpolation
zbMATH Keywords: big data
zbMATH Keywords: radial basis functions
zbMATH Keywords: layer by layer interpolation
reviewed by: Martin D. Buhmann
describes a project that uses: Matlab
MaRDI profile type: Publication
OpenAlex ID: W3010739090
cites work: Spectral convergence of multiquadric interpolation
cites work: Spherical interpolation using the partition of unity method: an efficient and flexible algorithm
cites work: Exponential convergence andH-c multiquadric collocation method for partial differential equations
cites work: Hermite interpolation with radial basis functions on spheres
cites work: Q3446085
cites work: Accuracy of radial basis function interpolation and derivative approximations on 1 D infinite grids
cites work: Q3457550
cites work: Miscellaneous error bounds for multiquadric and related interpolators
cites work: Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
cites work: Norm estimates for the inverses of a general class of scattered-data radial-function interpolation matrices
cites work: Error estimates and condition numbers for radial basis function interpolation
cites work: Scattered Data Approximation
cites work: Spectral approximation orders of radial basis function interpolation on the Sobolev space
DOI: 10.1016/J.APNUM.2020.03.009
description: scientific article; zbMATH DE number 7188159