Near-best operators based on a C-2 quartic spline on the uniform four-directional mesh
We present some results about the construction of quasi-interpolant operators based on a special C-2 quartic B-spline. We show that these operators, called near-best quasi-interpolants, have the best approximation order and small infinity norms. They are obtained by solving a minimization problem that admits always a solution. We give an error bound of these quasi-interpolants and we illustrate our results by a numerical example. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
b-splines box-splines subdivision scheme refinable function vector near-best quasi-interpolants