关于有理插值方法的若干分析-计算数学专业论文.docxVIP

Study on rational interpolation method ABSTRACT There is a lot of nonlinear problems， which need to be solved in the social science and natural science, these problems have become one of the main direction of research. Rational function approximation is as one of the typical nonlinear approximation, which is more efficient and can better response function of characteri stics and has a strong practice, Therefore, it has been widely appli ed in system control、 computer aided geometric design 、 digital filtering 、 numerical approximation and function approximation and so on. Constructed rational function which is based continued fraction rational interpolation has high precision, and barycentric rational interpolation has smaller calculation and more accuracy. When we select the appropriate weight , it can avoid poles .So based on Thiele type continued fraction interpolation and barycentric rational interpolation, This thesis made further research on rational interpolation method. The main work is as follows: The thesis summarizes the research background and introduces the definition and properties of the rational interpolation. Based on Thiele type continued fraction rational interpolation an d Generalized barycentric rational interpolation, we construct Barycentric -Thiele type blending rational interpolation. Properties of the blending rational interpolation are presended such as characteristic and poles in the interpolation interval, And the error estimates are given. numerical examples will be the focus of Barycentric -Thiele type blending rational interpolation 、 Thiele type continued fraction interpolation and barycentric rational interpolation of the three comparison,these numerical examples are presented to verify the correctness and validity of this method. As Thiele type continued fraction interpolation and barycentric rational interpolation are framework,we construct Triple Barycentric -Thiele type blending rational interpolation. P