Fast algorithms for interpolation with L-splines for differential operators L of order 4 with constant coefficients
| Autor: | Kounchev, Ognyan, Render, Hermann, Tsachev, Tsvetomir |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In the classical theory of cubic interpolation splines there exists an algorithm which works with only $O\left( n\right)$ arithmetic operations. Also, the smoothing cubic splines may be computed via the algorithm of Reinsch which reduces their computation to interpolation cubic splines and also performs with $O\left( n\right)$ arithmetic operations. In this paper it is shown that many features of the polynomial cubic spline setting carry over to the larger class of $L$-splines where $L$ is a linear differential operator of order $4$ with constant coefficients. Criteria are given such that the associated matrix $R$ is strictly diagonally dominant which implies the existence of a fast algorithm for interpolation. Comment: 33 pages, 4 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|