Maximal approximation order for a box-spline semi-cardinal interpolation scheme on the three-direction mesh
Source: Advances in Computational Mathematics, Volume 22, Number 3, April 2005 , pp. 275-298(24)
Abstract:Let M be the centred 3-direction box-spline whose direction matrix has every multiplicity 2. A new scheme is proposed for interpolation at the vertices of a semi-plane lattice from a subspace of the cardinal box-spline space generated by M. The elements of this ‘semi-cardinal’ box-spline subspace satisfy certain boundary conditions extending the ‘not-a-knot’ end-conditions of univariate cubic spline interpolation. It is proved that the new semi-cardinal interpolation scheme attains the maximal approximation order 4.
Document Type: Research Article
Affiliations: 1: Department of Applied Mathematics, University of Leeds, LS2 9JT, UK, Email: firstname.lastname@example.org 2: Numerical Geometry Ltd., Lode, Cambridge, CB5 9EP, UK, Email: email@example.com
Publication date: 2005-04-01