Minimal degree interpolation spaces with respect to a nite set of points are subspaces of multivariate polynomials of least possible degree for which Lagrange interpolation with respect to the given points is uniquely solv-able and degree reducing. This is a generalization of the concept of least interpolation introduced by de Boor and Ron. This paper investigates the behavior of Lagrange inter...

Combining Newton and Lagrange interpolation, we give q-identities which generalize results of Van Hamme, Uchimura, Dilcher and Prodinger.

In this paper, Field-Programmable Gate Array (FPGA) implementation-based image demosaicing is carried out. The Newton Gregory interpolation algorithm designed based on FPGA frame work. Interpolation the method of assessing value a function for any in-between self-regulating variable, whereas computing outside specified range named extrapolation. natural images are collected from Kodak database ...

Abstract. In 1986, Irvine, Marin, and Smith proposed a Newton-type method for shapepreserving interpolation and, based on numerical experience, conjectured its quadratic convergence. In this paper, we prove local quadratic convergence of their method by viewing it as a semismooth Newton method. We also present a modification of the method which has global quadratic convergence. Numerical exampl...

Abstract An inverse central ordering of the nodes is proposed for Newton interpolation formula. This may improve stability certain distributions nodes. For equidistant nodes, an upper bound conditioning provided. close to in Lagrange formula, whose lowest. related a pivoting strategy matrix elimination procedure called Neville elimination. The results are illustrated with examples.

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...