Block Based Blending Osculatory Interpolation

The summaries of this dissertation are the researches on the block based blending osculatory interpolation, which include block based Lagrange-Salzer blending osculatory rational interpolation and block based Newton-like blending osculatory interpolation.we combine continued fraction osculatory interpolation with the Lagrange's polynomial by dividing blocks and construct a kind of block based Lagrange-Salzer blending osculatory rational interpolation. The new construction method is more flexible and the traditional Salzer continued fraction interpolation is a special case. Some numerical examples are given to illustrate the effectiveness of the method in this paper.With the Newton's interpolating formation, we construct a kind of block based Newton-like blending osculatory interpolation. The interpolation provides us with many flexible interpolation schemes for choices which include the expansive Newton's polynomial interpolation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.