@article{2cc56d23d299435b9e98e8c1eec50d3e,
title = "A study on multivariate interpolation by increasingly flat kernel functions",
abstract = "In this paper, we improve upon some observations made in recent papers on the subject of increasingly flat interpolation. We shall establish that the corresponding Lagrange functions converge both for a finite set of functions (collocation matrix) and also for kernels (Fredholm matrix). In our analysis, we use a finite Maclaurin expansion of a multivariate function with remainder and some additional matrix theoretic facts.",
keywords = "Cauchy-Binet formula, Collocation matrix, L'Hospital's rule, Multivariate kernel interpolation, Radial basis function, Wronskian",
author = "Lee, {Yeon Ju} and Micchelli, {Charles A.} and Jungho Yoon",
note = "Funding Information: The authors are grateful to the anonymous referee for the valuable suggestions on this paper. Jungho Yoon was supported by Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology . C. Micchelli is supported in part by the US National Science Foundation under grant DMS-1115523 . Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",
year = "2015",
month = jul,
day = "1",
doi = "10.1016/j.jmaa.2015.02.006",
language = "English",
volume = "427",
pages = "74--87",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",
}