In this paper, we study the C1 Hermite interpolation problem using Minkowski Pythagorean Hodograph (MPH) quartics in R2,1. As a preliminary step, we characterize MPH curves in R2,1 by the roots of the hodographs of their complexified spine curves. We present two schemes for this interpolation problem: one is a subdivision scheme using direct C1 interpolation and the other is a two step scheme u...

Several optimal eighth order methods to obtain simple roots are analyzed. The methods are based on two step, fourth order optimal methods and a third step of modified Newton. The modification is performed by taking an interpolating polynomial to replace either f ðznÞ or f ðznÞ. In six of the eight methods we have used a Hermite interpolating polynomial. The other two schemes use inverse interpo...

The B-spline representation for divided di erences is used, for the rst time, to provide Lp-bounds for the error in Hermite interpolation, and its derivatives, thereby simplifying and improving the results to be found in the extensive literature on the problem. These bounds are equivalent to certain Wirtinger inequalities (cf. [FMP91:p66]). The major result is the inequality jf(x) H f(x)j n 1=q...

Abstract In this paper, a new approach to improve univariate multiquadric operators is surveyed. The presented scheme is obtained by using Hermite interpolating polynomials where the function is approximated by generalized LB quasi-interpolation operator. Error analysis shows that the convergence rate depends on the shape parameter c. Thus, our operators could provide the desired smoothness and...