[Her13] F.Hernoux, R.Béarée, L.Gajny, E.Nyiri, J.Bancalin, O.Gibaru, Leap Motion pour la capture de mouvement 3D par spline L1. Application à la robotique. GTMG 2013, Marseille, 27-28 mars 2013 [Gib1899] J. Willard Gibbs, lettre à l’éditeur, Nature 59 (April 27, 1899) 606. [Lav00] J.E. Lavery, Univariate Cubic Lp splines and shape-preserving multiscale interpolation by univariate cubic L1 splin...

A well-known approach to image interpolation is cubic convolution, in which the ideal sinc function is modelled by a finite extent kernel, which consists of piecewise third order polynomials. In this paper we show that the concept of cubic convolution can be generalized. We derive kernels of up to ninth order and compare them both mutually and to cardinal splines of corresponding orders. From s...

A trivariate Lagrange interpolation method based on C cubic splines is described. The splines are defined over a special refinement of the Freudenthal partition of a cube partition. The interpolating splines are uniquely determined by data values, but no derivatives are needed. The interpolation method is local and stable, provides optimal order approximation, and has linear complexity.

In this paper, we will apply cubic B-splines on a uniform mesh to explore the numerical solutions and numerical derivatives of a class of nonlinear second-order boundary value problems with two dependent variables. Our new method is based on the cubic spline interpolation. The analytical solutions and any-order derivatives can be well approximated with 4th order accuracy. Furthermore, our new m...

Genome-scale microarray datasets are noisy. We have previously reported an algorithm that yields highly specific genome-scale discovery of states of genetic expression. In its original implementation, the algorithm computes parameters by globally fitting data to a function containing a linear combination of elements that are similar to the Hill equation and the Michaelis-Menten differential equ...

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 ...