Abstract
Generalized monosplines of least norm are shown to exist and to determine optimal approximation processes such as numerical integration, interpolation and best approximating spaces. This extends various classical results related to monosplines and perfect splines, which are particular cases of generalized monosplines. The analysis here also provides for a unified treatment of the two classical classes of monosplines and perfect splines of least norm, and of their extremal properties.
| Original language | English |
|---|---|
| Pages (from-to) | 137-154 |
| Number of pages | 18 |
| Journal | Constructive Approximation |
| Volume | 1 |
| Issue number | 1 |
| DOIs | |
| State | Published - Dec 1985 |
Keywords
- AMS classification: 41A15, 41A5, 41A65
- Extended totally positive kernels
- Monosplines
- Monotone norms
- N-widths
- Optimal interpolation
- Optimal quadrature formulas
- Optimal spaces
- Perfect splines