Lp-error bounds for Hermite interpolation and the associated Wirtinger inequalities

An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves

In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...

Some extended Simpson-type inequalities and applications

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

Error bounds for bivariate piecewise hermite interpolation

Hermite and Hermite-fejér Interpolation of Higher Order and Associated Product Integration for Erdős Weights

Using the results on the coefficients of Hermite-Fejér interpolations in [5], we investigate convergence of Hermite and Hermite-Fejér interpolation of order m, m = 1, 2, . . . in Lp(0 < p < ∞) and associated product quadrature rules for a class of fast decaying even Erdős weights on the real line.

UNIVERSITY OF WISCONSIN-MADISON CENTER FOR THE MATHEMATICAL SCIENCES A multivariate form of Hardy's inequality and Lp-error bounds for multivariate Lagrange interpolation schemes

valid for f 2 Lp(IR ) and an arbitrary nite sequence of points in IR, is discussed. The linear functional f 7! R f was introduced by Micchelli [M80] in connection with Kergin interpolation. This functional also naturally occurs in other multivariate generalisations of Lagrange interpolation, including Hakopian interpolation, and the Lagrange maps of Section 5. For each of these schemes, (1) imp...