A simple algorithm for the construction of the unique Hermite interpolating polynomial (in the special case, the Lagrange interpolating polynomial) is given. The interpolation matches preassigned data of function and consecutive derivatives on a set of points laying on several radial rays. This algorithm is realized in the software package Mathematica.

We discuss multiscale representations of discrete manifold-valued data. As it turns out that we cannot expect general manifold-analogues of biorthogonal wavelets to possess perfect reconstruction, we focus our attention on those constructions which are based on upscaling operators which are either interpolating or midpoint-interpolating. For definable multiscale decompositions we obtain a stabi...

| We extend the classical interpolation method to generalized interpolation. This extension is done by replacing the interpolating function by a non-interpolating function that is applied to preeltered data, in order to preserve the interpolation condition. We show, both theoretically and practically, that this approach performs much better than classical methods, for the same computational cost.

Using recent results where we constructed refinable functions for composite dilations, we construct interpolating multiscale decompositions for such systems. Interpolating wavelets are a well-known construction similar to the usual L2-theory but with L2-projectors onto the scaling spaces replaced by L∞projectors defined by an interpolation procedure. A remarkable result is that this much simple...

Abstract : A new weighted bivariate blending rational spline with parameters is constructed based on function values of a function only. The interpolation is C1 in the whole interpolating region under the condition which free parameters is not limited. This study deals with the bounded property of the interpolation. In order to meet the needs of practical design, an interpolation technique is e...

This paper presents a new weighted bivariate blending rational spline interpolation based on function values. This spline interpolation has the following advantages: firstly, it can modify the shape of the interpolating surface by changing the parameters under the condition that the values of the interpolating nodes are fixed; secondly, the interpolating function is C-continuous for any positiv...

In an effort to extend the classical lagrangian interpolation tools, new interpolating methods that use general interpolating functions are explored. The Generalized Empirical Interpolation Method (GEIM) belongs to this class of new techniques. It generalizes the plain Empirical Interpolation Method [1] by replacing the evaluation at interpolating points by application of a class of interpolati...