Barycentric Blending Rational Interpolation Over Triangular Grids

In the field of mathematics, interpolation is an indispensable tool.As is known to us although Polynomial Interpolation the structure is simple and easy to construct, when the number of the interpolation function is higher may be product Runge phenomenon. Such as:Lagrange interpolation, Newton interpolation, and Hermite interpolation. Rational interpolation convergence rate is fast and is not" Runge "phenomenon but it may not be able to avoid the existence of the pole and unattainable.Barycentric Rational Interpolation can be effectively overcome the above defects and different interpolation weight decision interpolation function effect,So the key lies in the weight selection of Barycentric Rational Interpolation. In this paper, the bivariate barycentric-Newton blending rational interpolant is constructed based on the right triangular grid.The objective function is Lebesgue constant minimizing, at the same time to join some no poles,no unattainable interpolation function and constraint conditions of feasible solution only optimization model is established. Not only inherited Barycentric Rational Interpolation advantages:no unattainable points and pole as well as good stability, and can target the unknown function interpolation. Add binary partial derivative as constraint conditions, an optimized model can effectively adjust the shape of triangular mesh interpolation function. At last, with plenty of example shows that the method is effective and feasible.