Odd-Degree Spline Interpolation at a Biinfinite Knot Sequence.
Abstract
It is shown that for an arbitrary strictly increasing knot sequence t = (t sub 1) infinity to minus infinity and for every i, there exists exactly one fundamental spline L sub i (i.e., L sub i)(t sub j) = delta sub ij, all j), of order 2r whose r-th derivative is square integrable. Further, L(r) sub i (x) is shown to decay exponentially as x moves away from t sub i, at a rate which can be bounded in terms of r alone. This allows one to bound odd-degree spline interpolation at knots on bounded functions in terms of the global mesh ratio M Sub t: = sup sub i, j Delta t sub i/Delta t sub j. A very nice result of Demko's concerning the exponential decay away from the diagonal of the inverse of a band matrix is slightly refined and generalized to (bi)infinite matrices.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1976
- Accession Number
- ADA031958
Entities
People
- Carl R. de Boor
Organizations
- University of Wisconsin–Madison