Nonlinear Approximation from Differentiable Piecewise Polynomials
Abstract
We study nonlinear n-term approximation in L(sub p) (all Real Numbers[expn 2]) (0 < p </= infinity) from hierarchical sequences of stable local bases consisting of differentiable (i.e., C[expn r] with r>/+ 1) piece-wise polynomials (splines). We construct such sequences of bases over multilevel nested triangulations of all Real Numbers(expn 2), which allow arbitrarily sharp angles. To quantize nonlinear n-term spline approximation, we introduce and explore a collection of smoothness spaces (B-spaces). We utilize the B-spaces to prove companion Jackson and Bernstein estimates and then characterize the rates of approximation by interpolation. Even when applied on uniform triangulation with well-known families of basis functions such as box splines, the results give a more complete characterization of the approximation rates than the existing ones involving Besov spaces. Our results can easily be extended to properly defined multilevel triangulations in all Real Numbers (expn d), d > 2.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2002
- Accession Number
- ADA640663
Entities
People
- Oleg Davydov
- Pencho Petrushev
Organizations
- University of South Carolina