@inproceedings{b5c60485074d4287acbdc3af9d017b97,
title = "Spline Approximation on Sparse Grids",
abstract = "We present a compact sparse grid operator to multivariate functions on [0,1]d using the combination technique and tensor product spline interpolation. The construction is based on univariate spline interpolation using full end knots supported on [0,1], and the not-a-knot end condition. In this paper, we provide details for the construction of sparse grids and our spline interpolants, and a demonstration of computational performance. The paper includes a formula for counting the grid points in sparse grids, and an estimate for the number of computations in computing sparse spline interpolants. The results show that our construction performs at the level we expect based on other methods in the literature.",
keywords = "Approximation, Interpolation, Sparse grids, Splines",
author = "Scott Kersey and Chukwugozirim Ehirim",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 1st Southern Georgia Mathematics Conference, SGMC 2021 ; Conference date: 02-04-2021 Through 03-04-2021",
year = "2024",
doi = "10.1007/978-3-031-69710-4_12",
language = "English",
isbn = "9783031697098",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "285--299",
editor = "Divine Wanduku and Shijun Zheng and Zhan Chen and Andrew Sills and Haomin Zhou and Ephraim Agyingi",
booktitle = "Applied Mathematical Analysis and Computations II - 1st SGMC",
address = "Germany",
}