On optimal triangular meshes for minimizing the gradient error.
We consider triangulations formed by triangular elements. For the standard linear interpolation operator we prove the interpolation order to be for provided the corresponding family of triangulations is only semiregular. In such a case the well-known Zlámal’s condition upon the minimum angle need not be satisfied.
We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.
2000 Mathematics Subject Classification: 41A05.For the Hermite interpolation polynomial, Hm(x) we prove for any function f of C^(2q) ([−1, 1]) and any s = 0, 1, 2, . . . , q , where q is a fixed integer that ...
This survey is a tribute to Géza Grünwald and Józef Marcinkiewicz dealing with the so called Grünwald-Marcinkiewicz Theorem.