Research On General Frames Of Interpolants

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。...