sk-Spline interpolation on R^n
F. Jarad, A. Kushpel, J. Levesley, K. Tas
TL;DR
This paper introduces sk-splines on R^n, providing representations for cardinal sk-splines on specific point sets that are useful for high-dimensional problems, extending concepts similar to Korobov grids.
Contribution
It establishes a new framework for sk-splines on R^n and derives representations for cardinal sk-splines on specialized point sets, generalizing Korobov's grids.
Findings
Representation formulas for cardinal sk-splines on AZ^n sets
Extension of Korobov's grids to R^n for high-dimensional interpolation
Potential applications in high-dimensional approximation problems
Abstract
The main aim of this article is to introduce sk-splines on R^n and establish representations of cardinal sk-splines with knots and points of interpolation on the sets AZ^n, where A is an arbitrary nonsingular matrix. Such sets of points are analogs for R^n of number theoretic Korobov's grids on the torus and proved to be useful for problems of very high dimensionality.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Digital Filter Design and Implementation · Advanced Numerical Methods in Computational Mathematics