| At present,there are a lot of nonlinear problems in scientific practice.In the methods of solving the nonlinear problems,rational function interpolation is one of the hot topics in research,because of its good flexibility and high approximation precision.It has been widely used in approximate approximation and scientific research.There are many methods for constructing rational interpolation function.Among them,the most commonly used are continued fractions.Because that the characteristics of the continued fractions make the constructed rational functions have strong recursion,and it is easy to calculate the coefficients.In this paper,we first give some background and theoretical knowledge related to continued fractions and rational interpolation.Then we come up with the Stieltjes-Thiele type binary mixed rational interpolation based on the Stieltjes type and Thiele type continued fraction by defining the appropriate inverse difference in the third chapter.Then,we prove that this kind of rational interpolation meets the conditions given and we get the characteristic and error theorems.And two examples are given,the required coefficients are obtained by the inverse quotient formula in the definition.So,the validity of this rational interpolation method is illustrated.In the fourth chapter,on the basis of the rational interpolation that is proposed in the third chapter,the function form and the inverse difference formulas are changed,and then it is mixed with the generalized barycentric rational interpolation to obtain the binary barycentric Stieltjes-Thiele type rational interpolation that satisfies the interpolation.The error theorem is given.Finally,according to the discrete interpolation points and interpolation points of the continuous function,two examples are given,and the inverse quotient formula is still used to obtain the coefficients.The effectiveness of the rational interpolation of the barycentric rational interpolation constructed in chapter four is verified. |
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