Abstract. In this paper, first free parameters are constrained in the description of rational cubic function [6] to preserve the shape of data that lies above the straight line. Then, rational cubic function is extended to rational bicubic partially blended function (Coons patches). A local positivity preserving scheme is developed for positive data by making constraints on free parameters in t...

This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil (A,B). Based on Zolotarev’s best rational function approximations of the signum function and conformal mapping techniques, we construct the best rational function approximation of a rectangular function supported on an arbitrary interval. This new best rational func...

In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f) cannot be computed. In the case of a synchronous rat...

A noncommutative rational function which is regular at 0 can be expanded into a noncommutative formal power series. In fact, by the results of Kleene, Schützenberger, and Fliess, a noncommutative formal power series is rational (i.e., belongs to the smallest subring containing the noncommutative polynomials and closed under the inversion of invertible power series) if and only if the correspond...

This paper deals with the shape preserving C rational cubic interpolation. The developed rational cubic interpolating function has only one free parameter. The approximation order of rational cubic function is investigated and range of optimal error constant is determined. Moreover, positive, constrained and monotone data preserving schemes are developed. 2000 Mathematics Subject Classification...

The physical and generalized sensor models are two widely used imaging geometry models in the photogrammetry and remote sensing. Utilizing the rational function model (RFM) to replace physical sensor models in photogrammetric mapping is becoming a standard way for economical and fast mapping from high-resolution images. The RFM is accepted for imagery exploitation since high accuracies have bee...

In this paper rational approximation of solutions to nonlinear optimal control problems is considered. A computational procedure is presented that makes it possible to compute a rational function that approximates the true optimal cost function. It is shown that the rational function has the same series expansion around the origin as the true solution. Finally, two examples are given that compa...

In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f) cannot be computed. In the case of a synchronous rat...

The conchoid surface G of a given surface F with respect to a point O is roughly speaking the surface obtained by increasing the radius function of F with respect to O by a constant d. This paper studies real rational ruled surfaces in this context and proves that their conchoid surfaces possess real rational parameterizations, independently on the position of O. Thus any rational ruled surface...