We describe an efficient and accurate numerical method for computing smooth approximations to invariant manifolds of planar maps, based on geometric modeling ideas from Computer Aided Geometric Design (CAGD). The unstable manifold of a hyperbolic fixed point is modeled by a piecewise Bézier interpolant (a Catmull–Rom spline) and properties of such curves are used to define a rule for adaptively...

We present a general and simple procedure to construct quasi-interpolants in hierarchical spaces, which are composed of a hierarchy of nested spaces. The hierarchical quasi-interpolants are described in terms of the truncated hierarchical basis. Once for each level in the hierarchy a quasi-interpolant is selected in the corresponding space, the hierarchical quasi-interpolants are obtained witho...

In this paper, we study the global behavior of a function that is known to be small at a given discrete data set. Such a function might be interpreted as the error function between an unknown function and a given approximant. We will show that a small error on the discrete data set leads under mild assumptions automatically to a small error on a larger region. We will apply these results to spl...

Abstract Today’s typical application of geometric morphometrics to a quantitative comparison organismal anatomies begins by standardizing samples homologously labelled point configurations for location, orientation, and scale, then renders the ensuing comparisons graphically thin-plate spline as applied group averages, principal components, regression predictions, or canonical variates. The sca...

When fitting a parametric curve through a sequence of points, it is important in applications that the curve should not exhibit unwanted oscillations. In this paper we take the view that a good curve is one that does not deviate too far from the data polygon: the polygon formed by the data points. From this point of view, we study periodic cubic spline interpolation and derive bounds on the dev...

Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing optimal approximating spline for each function proved to be very hard. In fact, no polynomial time algorithm of adaptive spline approximation can be designed...

Abstract In the proposed work, an improvised collocation technique with cubic B-spline as basis functions is applied to obtain numerical solution of non-linear generalized Burgers’–Huxley equation, which has application in soliton theory. this technique, posteriori corrections are made interpolant and its higher-order derivatives, leads enhancement order convergence spatial domain. The temporal...

We use C 1 quintic superspline functions to interpolate any given scattered data. The space of C 1 quintic superspline functions is introduced in Lai and LeMehaute'99] and is an improvement of the Alfeld scheme of 3D scattered data interpolation. We have implemented the spline space in MATLAB and tested for the accuracy of reproduction of all quintic polynomials. We present some numerical evide...

V. Torra in [8] presents an algorithm for constructing Weighted OWA operators [7] using interpolation (De9nition 1 in [8]). His method relies on the construction of a monotone increasing functionW (x) that interpolates the points (i=n; ∑ j6i wj) together with the origin, where the weights wj denote relative importance or reliability of information sources. In addition to being monotone, the fun...

We generalize the transfinite triangular interpolant of (Nielson, 1987) in order to generate visually smooth (not necessarily polynomial) local interpolating quasi-optimal triangular spline surfaces. Given as input a triangular mesh stored in a half-edge data structure, at first we produce a local interpolating network of curves by optimizing quadratic energy functionals described along the arc...