In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative [Formula: see text] by Hermite interpolation operator [Formula: see text] based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some results are considered to be an improvement over those obtained in Al-Khaled and Khalil (Numer Func...

In recent years, a wide range of generalized barycentric coordinates has been suggested. However, all of them lack control over derivatives. We show how the notion of barycentric coordinates can be extended to specify derivatives at control points. This is also known as Hermite interpolation. We introduce a method to modify existing barycentric coordinates to higher order barycentric coordinate...

Based on the technique of C-shape G Hermite interpolation by cubic Pythagorean-Hodograph (PH) curve, we present a simple method for Cshape G Hermite interpolation by rational cubic Bézier curve. The method reproduces a circular arc when the input data come from it. Both the Bézier control points, which have the well understood geometrical meaning, and the weights of the resulting rational cubic...

A cubic Hermite approximation for two-dimensional boundary integral analysis is presented. The method differs from previous Hermite interpolation algorithms in that the gradient equations are sparse, significantly reducing the computational cost, and in that information about the surface normals is incorporated to effect a cubic interpolation of the geometry. A motivation for the development of...

This work suggests a parallel algorithm for Hermite interpolation on Extended Fibonacci Cube (n) EFC1 . The proposed algorithm has 3 phases: initialization, main and final. The main phase of the algorithm involves 3 2  N multiplications, N additions, N 2 subtractions and N divisions. In final phase we propose an efficient algorithm to accumulate the partial sums of Hermite interpolation in 2 )...

In this paper the capacity of different interpolation techniques aimed at wow defect reduction is examined. Involved are: linear interpolation, two polynomial based interpolation methods (Hermite and spline) and the windowed sinc-based method. The performance of a synthetic audio signal restored using incommensurate resampling for wow cancellation is evaluated on the basis of standard audio def...

Inverse solutions to interpolation techniques in computer graphics may increase the accuracy of the rendered frames. An example is the use of an arbitrary time stamp in time interpolation to evaluate the t-parameter, which in turn can be used for time-variant spatial interpolation. In this paper, an analytic inverse is presented for a shape-preserving piecewise cubic Hermite interpolant, used i...