List decoding may be translated into a bivariate interpolation problem. The interpolation problem is to find a bivariate polynomial of minimal weighted degree that interpolates a given set of pairs taken from a finite field. We present a behavioral approach to this interpolation problem. With the data points we associate a set of trajectories. For this set of trajectories we construct the Most ...

In this paper a new parallel algorithm for the computation of the inverse of a bivariate polynomial matrix are presented. The parallel algorithm based on the technique evaluation-interpolation and for the part of interpolation uses the Newton bivariate polynomial interpolation. The algorithm is applied to the programming environment of MATLAB with Parallel Computing Toolbox and is compared to t...

This paper presents a new method for image zooming. The new method is different from the traditional polynomial interpolation technique. A bivariate rational interpolation is used in the new method. Using the bivariate rational interpolation is more effective than the polynomial interpolation for image zooming, especially in processing the borders of the source image. The bivariate rational int...

In this paper, we present the design of a simultaneous compensator for a segment of systems based on an interpolation method with stable polynomial interpolants. This problem leads to formulate conditions of polynomial divisibility in the case of the simultaneous control as a polynomial interpolation issue. The feasibility and infeasibility of the approach is also analyzed. Finally, an algorith...

Let Aρ denote the set of functions analytic in |z| < ρ but not on |z| ρ 1 < ρ < ∞ . Walsh proved that the difference of the Lagrange polynomial interpolant of f z ∈ Aρ and the partial sum of the Taylor polynomial of f converges to zero on a larger set than the domain of definition of f . In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and H...

In a recent paper, Y. Xu proposed a set of Chebyshev-like points for polynomial interpolation on the square [−1, 1]. We have recently proved that the Lebesgue constant of these points grows like log of the degree (as with the best known points for the square), and we have implemented an accurate version of their Lagrange interpolation formula at linear cost. Here we construct non-polynomial Xu-...

In this paper, we give new sparse interpolation algorithms for black box polynomial f whose coefficients are from a finite set. In the univariate case, we recover f from one evaluation of f(β) for a sufficiently large number β. In the multivariate case, we introduce the modified Kronecker substitution to reduce the interpolation of a multivariate polynomial to the univariate case. Both algorith...

Abstract: A new basis of interpolation points for the special case of the Newton two variable polynomial interpolation problem is proposed. This basis is implemented when the upper bound of the total degree and the degree in each variable is known. It is shown that this new basis under certain conditions (that depends on the degrees of the interpolation polynomial), coincides either with the kn...

An interpolation polynomial of order N is constructed from p indepen­ dent subpolynomials of order n '" Nip. Each such subpolynomial is found independently and in parallel. Moreover, evaluation of the polynomial at any given point is done independently and in parallel, except for a final step of summation of p elements. Hence, the algorithm has almost no commu­ ,:.. nication overhead and can be...

The present survey collects some recent results on barycentric interpolation showing the similarity to the corresponding Lagrange (or polynomial) theorems. Namely we state that the order of the Lebesgue constant for barycentric interpolation is at least log n; we state a Grünwald–Marcinkiewicz type theorem for the barycentric case; moreover we define a Bernstein type process for the barycentric...