On Lagrange and Hermite Interpolation in Rk.
The uniform convergence of a sequence of Lienhard approximation of a given continuous function is proved. Further, a method of numerical integration is derived which is based on the Lienhard interpolation method.
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 ...