【作者】 邹乐；

【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】 本文主要讨论了二元插值的一般框架问题,其主要内容包括二元插值一般框架的一个注记、对称型有理插值的框架以及基于块的混合有理插值的一般结构。通过引进新的参数将檀结庆和方毅研究的二元插值的一般框架做进一步的推广和改进,使之可以用来处理带不可达点和逆差商不存在的插值问题,并将其推广至多元情形和基于块的混合有理插值情形,包含近年来人们研究的多种插值格式,如修正Thiele型连分式混合插值,基于块的牛顿型混合有理插值,基于块的Thiele型混合有理插值等。通过引进新的参数将檀结庆和方毅研究的二元对称型插值的一般框架做进一步的推广和改进,包含近年来赵前进、王家正、Kh.I.Kuchmins’ka,S.M.Vonza等人所研究的几种对称插值格式,并给出了几种新形式的对称型混合有理插值格式。将S.W.Kahng研究的插值的一种显示表达式进行改进和推广,构造了基于块的一元插值函数的一般结构,这种插值结构不仅包含了S.W.Kahng研究的显示公式,而且包含基于块的牛顿型混合有理插值,基于块的Thiele型混合有理插值以及Thiele-Werner型切触有理插值,此外还可以通过对参数的选取获得其它类型的插值函数。此外还推广S.W.Kahng研究的显示公式到多元情形,研究了二元情形的插值框架,插值定理,对偶插值格式,包括的特殊插值格式,并给出了这种插值框架的误差估计。更多还原

【Abstract】 The summaries of this dissertation are the researches on general frames of bivariate interpolant, which include note on general frames of bivariate interpolant, general frames of symmetry rational interpoaltion and general structures of black based interpolational function。A new general frame is established by introducing multiple parameters , which is extensions and improvements of those for the general frames studied by Tan and Fang, and can be used to deal with the interpolant problem when inverse differences are nonexistent or meeting unattainable points。We extend the general frames to multivariable case and block based blending rational interpolation case。Modify Thiele-type continued fraction blending interpolation, block based blending rational interpolation are special cases of the general frames。Numerical examples are given to show the effectiveness of the results。A new symmetry general frame is established by introducing multiple parameters, which is extensions and improvements of those for the general frames studied by Tan and Fang, the symmety interpolation formulae studied by Kh.I.Kuchmins’ka, S.M.Vonza, Zhao Qianjin, Wang Jiazheng etc. are special cases of the symmetry general frame, and give several symmetry blending rational interpolations of new form.We extend and improved the results of S.W.Kahng, construct general structure of one variable interpolation function, which not only include the results of S.W.Kahng. but also embody block based Newton-like blending rational interpolation, block based Thiele-like blending rational interpolation, Thiele-Werner osculatory rational interpolation and some other class interpolation function。We also extend the general structure to multivariate case, disscuss general structure of bivariate interpolation function, interpolation theorem, special case, dual interpolation frames and error estimation。Clearly, our method offers many flexible interpolation schemes for choices。更多还原