Bivariate composite vector valued rational interpolation

Bivariate composite vector valued rational interpolation

In this paper we point out that bivariate vector valued rational interpolants (BVRI) have much to do with the vector-grid to be interpolated. When a vector-grid is well-defined, one can directly design an algorithm to compute the BVRI. However, the algorithm no longer works if a vector-grid is ill-defined. Taking the policy of “divide and conquer”, we define a kind of bivariate composite vector...

A new approach to vector-valued rational interpolation

In this work we propose three different procedures for vector-valued rational interpolation of a function F(z), where F : C → C , and develop algorithms for constructing the resulting rational functions. We show that these procedures also cover the general case in which some or all points of interpolation coalesce. In particular, we show that, when all the points of interpolation collapse to th...

Lebesgue Constant Minimizing Bivariate Barycentric Rational Interpolation

The barycentric form is the most stable formula for a rational interpolant on a finite interval. The choice of the barycentric weights can ensure the absence of poles on the real line, so how to choose the optimal weights becomes a key question for bivariate barycentric rational interpolation. A new optimization algorithm is proposed for the best interpolation weights based on the Lebesgue cons...

Bivariate Blending Thiele-Werner’s Osculatory Rational Interpolation

Application of a Bivariate Rational Interpolation in Image Zooming

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...