Hermite interpolation with symmetric polynomials associated with quadratic curves in \(\mathbb {R}^2\)
摘要
We study the Hermite interpolation problem on the spaces of symmetric bivariate polynomials. We construct regular Hermite interpolation schemes that solve the problem, where the interpolation points lie on the upper parts of symmetric quadratic curves and the derivatives are induced from the natural parametrization of the curves. We also give a Newton type formula for the interpolation polynomial.