This paper proposes a new image resizing method based on splines, which is constructed by the Thieletype continued fractions and the Newton interpolation. Like most interpolation techniques proposed in the past, this paper focuses on determining pixel values using the relationship between neighboring points. The interpolation is carried out by choosing the osculatory interpolants in every subin...

We consider the problem of growth of the sequence of Lebesgue constants corresponding to the Newton interpolation and estimate the growth of this sequence in the case of a nested family of Chebyshev's points.

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...

1 Plane Curves 2 1.1 Computation of Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Expansion at Simple Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Expansion at Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.3 Newton Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.4 Local...

Let T be a Jordan curve in the complex plane, and let Í) be the compact set bounded by T. Let / denote a function analytic on O. We consider the approximation of / on fî by a polynomial p of degree less than n that interpolates / in n points on T. A convenient way to compute such a polynomial is provided by the Newton interpolation formula. This formula allows the addition of one interpolation ...

More than a decade agao, Newton’s method has been proposed for constructing the convex best interpolant. Its local quadratic convergence has only been established recently by recasting it as the generalized Newton method for semismooth equations. It still remains mysterious that the Newton method coupled with line search strategies works practically well in global sense. Similar to the classica...

Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...