Abstract
It is known that shape preserving approximation has lower rates than unconstrained approximation. This is especially true for copositive and intertwining approximations. For f ∈ Lp, 1 ≤ p < ∞, the former only has rate ωφ (f, n-1)p, and the latter cannot even be bounded by C ||f||p. In this paper, we discuss various ways to relax the restrictions in these approximations and conclude that the most sensible way is the so-called almost copositive/intertwining approximation in which one relaxes the restriction on the approximants in a neighborhood of radius Δn(γj) of each sign change γj.
| Original language | English |
|---|---|
| Pages (from-to) | 213-236 |
| Number of pages | 24 |
| Journal | Journal of Approximation Theory |
| Volume | 96 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1999 |
Scopus Subject Areas
- Analysis
- Numerical Analysis
- General Mathematics
- Applied Mathematics
Keywords
- Almost copositive approximation
- Almost intertwining approximation
- Constrained approximation
- Degree of approximation
- Polynomials
- Sobolev space
- Splines