A New Approach to Bivariate Symmetry Blending Rational Interpolation

By introducing partial divided differences and partial inverse differences, using Newton interpolation, Thiele continued fraction interpolation and associate continued fraction interpolation, a new bivariate symmetry blending rational interpolation is constructed. We discuss recursive algorithm, interpolating theorem and give some remarks. A numerical example is given to show the effectiveness of the method. We extend the conclusion to vector valued, matrix valued case and the triangular net case.