A bivariate rational interpolation with a bi-quadratic denominator

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 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...

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...

A weighted bivariate blending rational interpolation based on function values

This paper presents a new weighted bivariate blending rational spline interpolation based on function values. This spline interpolation has the following advantages: firstly, it can modify the shape of the interpolating surface by changing the parameters under the condition that the values of the interpolating nodes are fixed; secondly, the interpolating function is C-continuous for any positiv...