Box splines
Quasi-interpolants associated with H-splines on a three-direction mesh
Proceedings of the 6th international congress on Computational and applied mathematics
Bernstein--Bézier representation and near-minimally normed discrete quasi-interpolation operators
Applied Numerical Mathematics
On Chebyshev-type discrete quasi-interpolants
Mathematics and Computers in Simulation
Minimizing the quasi-interpolation error for bivariate discrete quasi-interpolants
Journal of Computational and Applied Mathematics
On Chebyshev-type integral quasi-interpolation operators
Mathematics and Computers in Simulation
On near-best discrete quasi-interpolation on a four-directional mesh
Journal of Computational and Applied Mathematics
Near minimally normed spline quasi-interpolants on uniform partitions
Journal of Computational and Applied Mathematics
Near-best quasi-interpolants associated with H-splines on a three-direction mesh
Journal of Computational and Applied Mathematics
Optimal bivariate C1 cubic quasi-interpolation on a type-2 triangulation
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
A general method for constructing quasi-interpolation operators based on B-splines is developed. Given a B-spline @f in R^s, s=1, normalized by @?"i"@?"Z"^"s@f(@?-i)=1, the classical structure Q(f)@?@?"i"@?"Z"^"s@lf(@?+i)@f(@?-i), for a quasi-interpolation operator Q is considered. A minimization problem is derived from an estimate of the quasi-interpolation error associated with Q when @lf is a linear combination of values of f at points in some neighbourhood of the support of @f; or a linear combination of values of f and some of its derivatives at some points in this set; or a linear combination of weighted mean values of the function to be approximated. That linear functional is defined to produce a quasi-interpolant exact on the space of polynomials of maximal total degree included in the space spanned by the integer translates of @f. The solution of that minimization problem is characterized in terms of specific splines which do not depend on @l but only on @f.