| Affiliation: | (1) Department of Applied Mathematics, University of Leeds, LS2 9JT, UK;(2) Numerical Geometry Ltd., Lode, Cambridge, CB5 9EP, UK |
| 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.AMS subject classification 41A15, 41A05, 41A25, 41A63, 39A70, 47B35 |
