We discuss the implementation of a C quintic superspline method for interpolating scattered data in IR based on a modification of Alfeld’s generalization of the Clough-Tocher scheme described by Lai and LeMéhauté [4]. The method has been implemented in MATLAB, and we test for the accuracy of reproduction on a basis of quintic polynomials. We present numerical evidences that when the partition i...

Given a bivariate function f defined in a rectangular domain Ω, we approximate it by a C1 quadratic spline quasi-interpolant (QI) and we take partial derivatives of this QI as approximations to those of f. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary points, illustrated by a numerical example. ...

In this paper, planar parametric Hermite cubic interpolants with small curvature variation are studied. By minimization of an appropriate approximate functional, it is shown that a unique solution of the interpolation problem exists, and has a nice geometric interpretation. The best solution of such a problem is a quadratic geometric interpolant. The optimal approximation order 4 of the solutio...

For high dimensional problems, such as approximation and integration, one cannot afford to sample on a grid because of the curse of dimensionality. An attractive alternative is to sample on a low discrepancy set, such as an integration lattice or a digital net. This article introduces a multivariate fast discrete Walsh transform for data sampled on a digital net that requires only O(N logN) ope...

We consider the problem of thin plate spline interpolation to n equally spaced points on a circle, where the number of data points is suuciently large for work of O(n 3) to be unacceptable. We develop an iterative multigrid-type method, each iteration comprising ngrid stages, and n being an integer multiple of 2 ngrid?1. We let the rst grid, V 1 , be the full set of data points, V say, and each...

Nonlinear fractional differential equations are widely used to model real-life phenomena. For this reason, there is a need for efficient numerical methods solve such problems. In respect, collocation particularly attractive their ability deal with the nonlocal behavior of derivative. Among variety methods, based on spline approximations preferable since can be represented by local bases, thereb...

Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or steep gradient data, some artifacts can appear Gibbs phenomenon. Also, preservation data monotonicity is requirement applications, that property not automatically verified by interpolator. In this paper, we...

Sampling and reconstruction of generic multivariate functions is more efficient on non-Cartesian root lattices, such as the BCC (Body-Centered Cubic) lattice, than on the Cartesian lattice. We introduce a new n × n generator matrix A that enables, in n variables, for efficient reconstruction on the non-Cartesian root lattice An by a symmetric box-spline family M r . A2 is the hexagonal lattice ...