Lebesgue Constant Minimizing Shape Preserving Barycentric Rational Interpolation Optimization algorithm

The barycentric rational interpolation possesses various advantages in comparison with other interpolation, such as small calculation quantity, no poles and no unattainable points. It is definite when weights are given, so how to choose optimal weights becomes the key issue. A new optimization algorithm to compute the optimal weights was found by minimizing the Lebesgue constant. The biggest advantage of this algorithm is that the linearity of interpolation process with respect to the interpolated function is preserved. In this paper, we will study the shape control in barycentric rational interpolation under this new optimization algorithm, then numerical examples are given to shown the effectiveness of this algorithm.