Dichotomies for Band Matrices.
Abstract
Spline approximation is often most effective when the breakpoint (knot) sequence can be chosen suitably nonuniform. At the same time, standard spline approximation schemes (such as least-squares approximation by splines) are so far only known to be bounded as long as the breakpoint sequence is almost uniform. Any such bound is obtained (explicitly or implicitly) in terms of a bound on the inverse of certain matrices which are banded. Any attempt at establishing bounds for more general breakpoint sequences must therefore come to grips with the inverses of these band matrices. The hope is that Demko's discovery of the exponential decay of band matrix inverses will lead eventually to those desired bounds. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1980
- Accession Number
- ADA086373
Entities
People
- Carl R. de Boor
Organizations
- University of Wisconsin–Madison