Total Positivity of the Discrete Spline Collocation Matrix.
Abstract
Spline interpolation is an important tool of approximation. Usually, it costs less computation and yields a good approximation. The question of existence and uniqueness of such an interpolant is settled by the Schoenberg-Whitney Theorem, which is the basis for spline interpolation. There is a strong relationship between a spline and the coefficients in the expansion of the spline into a B-spline series. In many ways, the coefficient sequence behaves like the spline it represents. For this reason, it is called a discrete spline. In this paper, we develop several properties of discrete B-splines and prove the discrete analogue of the Schoenberg-Whitney theorem. It is expected that the result obtained here would play a role in discrete spline interpolation, discrete minimization and other related areas. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1982
- Accession Number
- ADA120994
Entities
People
- Rong-qing Jia
Organizations
- University of Wisconsin–Madison