
Accession Number : ADA116216
Title : Local Explicit ManyKnot Spline Hermite Approximation Schemes.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Qi,D X ; Zhou,S Z
PDF Url : ADA116216
Report Date : Apr 1982
Pagination or Media Count : 13
Abstract : Some authors considered operators of the form Omega f = sigma lambda i fN i,k, where (Ni,k) is a sequence of Bsplines and (lambda i) is a sequence of linear functionals. The variation diminishing method of Schoenberg (9, 5, 6), the quasiinterpolant of de Boor and Fix are wellknown. Such approximation schemes have several important advantages over spline interpolation. They can be constructed directly without matrix inversion, local error bounds can be obtained naturally. Omega i considered socalled manyknot splines which have many more knots than degrees of freedom and constructed the cardinal spline Omega f = sigma f(xi)qi,k, where qi,k is made up of Bsplines on a uniform partition, has small support and satisfies qi,k(xj) = sigma ij. Such an approximation operator reproduces appropriate classes of polynomials.
Descriptors : *Approximation(Mathematics), *Polynomials, *Operators(Mathematics), Degrees of freedom, Inversion, Matrices(Mathematics), Errors, Interpolation, Splines
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE