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Approximation of Irregular Geometric Data by Locally Calculated Univariate Cubic \(L^1\) Spline Fits
| Content Provider | Paperity |
|---|---|
| Author | Lavery, John Fang, Shu-cherng Wang, Ziteng |
| Abstract | \(L^1\) splines have been under development for interpolation and approximation of irregular geometric data. We investigate the advantages in terms of shape preservation and computational efficiency of calculating univariate cubic \(L^1\) spline fits using a steepest-descent algorithm to minimize a global data-fitting functional under a constraint implemented by a local analysis-based interpolating-spline algorithm on 5-node windows. Comparison of these locally calculated \(L^1\) spline fits with globally calculated \(L^1\) spline fits previously reported in the literature indicates that the locally calculated spline fits preserve shape on the average slightly better than the globally calculated spline fits and are computationally more efficient because the locally-calculated-spline-fit algorithm can be parallelized. |
| Starting Page | 5 |
| Ending Page | 14 |
| File Format | HTM / HTML |
| ISSN | 21985804 |
| DOI | 10.1007/s40745-014-0002-z |
| Issue Number | 1 |
| Journal | Annals of Data Science |
| Volume Number | 1 |
| e-ISSN | 21985812 |
| Language | English |
| Publisher | Springer Berlin Heidelberg |
| Publisher Date | 2014-04-25 |
| Access Restriction | Open |
| Subject Keyword | Shape preservation Univariate Approximation Spline fit $$l^1$$ l 1 spline Cubic spline |
| Content Type | Text |
| Resource Type | Article |
| Subject | Artificial Intelligence Business, Management and Accounting Statistics, Probability and Uncertainty Computer Science Applications |
