Total Positivity of the Spline Collocation Matrix.
Abstract
12010WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTERTotal Positivity of the Spline Collocation Matrix.Technical summary rept.,Sde Boor,Carl ;MRC-TSR-1396DA-31-124-ARO(D)-462*Splines, *Matrices(Mathematics), Inequalities, Approximation, Theorems, InterpolationCollocation method, Spline approximation, Spline interpolationAn elementary proof of the Schoenberg-Whitney Theorem concerning the existence and uniqueness of spline collocants is given. Karlin's proof of the total positivity of the collocation matrix involving B-splines is then adapted to give simple necessary and sufficient conditions for the existence and uniqueness of a spline collocant with some B-spline coefficients prescribed to be zero. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1973
- Accession Number
- AD0771395
Entities
People
- Carl R. de Boor
Organizations
- University of Wisconsin–Madison