On the Approximation Power of Local Least Squares Polynomials
Abstract
We discuss the relationship between the norm of the local discrete least squares polynomial approximation operator, the minimal singular value sigma(min)(Rho(sub Xi)) of the matrix Rho(sub Xi) of the evaluations of the basis polynomials, and the norming constant of the set of data points Xi with respect to the space of polynomials. Since these three quantities are equivalent up to bounded constants, and since sigma(min)(Rho(sub Xi)) can be efficiently computed, it is feasible to use sigma(min)(Rho(sub Xi)) as a tool for distinguishing good local point constellations, which is useful for scattered data fitting. In addition, we give a simple new proof of a bound by Reimer for the norm of the interpolation operators on the sphere and extend it to discrete least squares operators.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 2001
- Accession Number
- ADP013745
Entities
People
- Oleg Davydov
Organizations
- University of Giessen