Applied Mathematics Publications

Document Type

Article

Publication Date

11-2022

Journal

Journal of Approximation Theory

Volume

283

First Page

1

Last Page

8

URL with Digital Object Identifier

https://doi.org/10.1016/j.jat.2022.105810

Abstract

In this paper we introduce an apparently new spline-like interpolant that we call a compact cubic interpolant or compact cubic spline; this is similar to a cubic spline introduced in 1972 by Swartz and Varga, but has higher order accuracy at the edges. We argue that for nearly uniform meshes the compact cubic approach offers some potential advantages, and offers a simple way to treat the edge conditions, relieving the user of the burden of deciding to use one of the three standard options: free (natural), complete (clamped), or ``not-a-knot'' conditions. Finally, I establish that the matrices defining the compact cubic splines (equivalently, the fourth-order compact finite difference formulae) are totally nonnegative, if all mesh widths are the same sign, for instance if the mesh is real and nodes are numbered in increasing order.

Notes

This is the preprint version of the paper that is published at https://doi.org/10.1016/j.jat.2022.105810.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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