On near-best discrete quasi-interpolation on a four-directional mesh
Quasi-interpolation in two dimensions, for example, is a highly useful alternative to interpolation from spline or other function spaces. Its advantage is that no interpolation coefficients have to be computed; however, its construction depends on the choice of the linear operator which is to be applied to the approximand so that the quasi-interpolation can take place. (An example is a simple function evaluation at various points. Generally, only discrete operators are used in this article.) In this paper, the quasi-interpolants stem from polynomial spline spaces defined by four-direction meshes in two dimensions, and they are constructed to minimize the norm of the quasi-interpolation operator (comparable to the Lebesgue constant of the interpolation operator). It is in this sense that the quasi-interpolation is chosen -- as stated in the title -- to be near-best.
scientific article; zbMATH DE number 5650064