2020/11/23 by Rajesh Dachiraju, Dachiraju, Rajesh
Engineering · Mathematics · #42A10 42A15 35C99 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Fatigue and fracture mechanics #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2011.11258
openalex publication_date 2020/11/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
This paper addresses the problem of approximating a function of bounded\nvariation from its scattered data. Radial basis function(RBF) interpolation\nmethods are known to approximate only functions in their native spaces, and to\ndate, there has been no known proof that they can approximate functions outside\nthe native space associated with the particular RBF being used. In this paper,\nwe describe a scattered data interpolation method which can approximate any\nfunction of bounded variation from its scattered data as the data points grow\ndense. As the class of functions of bounded variation is a much wider class\nthan the native spaces of the RBF, this method provides a crucial advantage\nover RBF interpolation methods.\n