【作者】 李辰盛；

【导师】 唐烁；

【作者基本信息】 合肥工业大学 ， 计算数学， 2008， 硕士

【摘要】 本文主要讨论了基于块的混合切触插值问题,其主要内容包括基于块的Lagrange-Salzer混合切触有理插值和基于块的Newton型混合切触插值。利用分块的思想将连分式切触插值与Lagrange多项式相结合,构造了一种基于块的Lagrange-Salzer混合切触有理插值。该有理插值具有更好的灵活性,传统的Salzer连分式插值则是它的一个特例,同时数值例子表明该插值的有效性。借助于Newton插值的插值格式,构造了一种基于块的Newton型混合切触插值。由于采用了分块的方法,该插值提供了多种插值框架可供选择,其中扩展的Newton插值则是本文的一个特例。同时讨论了二元情况,给出的数值例子表明了该插值的有效性。更多还原

【Abstract】 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.更多还原