B-splines provide an accurate and efficient method for interpolating regularly spaced data. In this paper, I study the applicability of B-spline interpolation in the context of the inverse interpolation method for regularizing irregular data. Numerical tests show that, in comparison with lower-order linear interpolation, B-splines lead to a faster iterative conversion in under-determined proble...

Let A be a uniform algebra on the compact space X and σ a probability measure on X . We define the Hardy spaces H(σ) and the H(σ) interpolating sequences S in the p-spectrum Mp of σ. We prove, under some structural hypotheses on σ that ”Carleson type” conditions on S imply that S is interpolating with a linear extension operator in H(σ), s < p provided that either p = ∞ or p ≤ 2. This gives new...

The Lagrange representation of the interpolating polynomial can be rewritten in two more computationally attractive forms: a modified Lagrange form and a barycentric form. We give an error analysis of the evaluation of the interpolating polynomial using these two forms. The modified Lagrange formula is shown to be backward stable. The barycentric formula has a less favourable error analysis, bu...

Trivariate splines solve a special case of scattered data interpolation problem in the volume bounded by two concentric spheres. A triangulation ∆ of the unit sphere S is constructed based on the vertex set V. Given a partition P of the interval [1, R], let Sτ×ρ σ×δ be the space of the spherical splines of degree σ and smoothness τ over ∆ tensored with the univariate radial splines of degree δ ...

Animation is useful in user interfaces, especially for representing dynamic features. However, it is often difficult and laborious to create animation in an existing user interface environment. In this research, we extend our bi-directional translation model to deal with animations. The new model incorporates the notion of time, and includes operations defined for each representation in the mod...

We investigate here the interpolation conditions connected to an interpolating functionQ obtained as a Linear Fractional Transformation of another function S. In general, the degree ofQ is equal to the number of interpolating conditions plus the degree of S. We show that, if the degree of Q is strictly less that this quantity, there is a number of complementary interpolating conditions which ha...