Some Study On Rational Interpolation

There is a lot of nonlinear problems，which need to be solved in the social scienceand natural science, these problems have become one of the main direction of research.Rational function approximation is as one of the typical nonlinear approximation, whichis more efficient and can better response function of characteristics and has a strongpractice, Therefore, it has been widely applied in system control、 computer aidedgeometric design、 digital filtering、 numerical approximation and functionapproximation and so on. Constructed rational function which is based continuedfraction rational interpolation has high precision, and barycentric rational interpolationhas smaller calculation and more accuracy. When we select the appropriate weight, itcan avoid poles.So based on Thiele type continued fraction interpolation andbarycentric rational interpolation, This thesis made further research on rationalinterpolation method. The main work is as follows:1The thesis summarizes the research background and introduces the definition andproperties of the rational interpolation.2Based on Thiele type continued fraction rational interpolation and Generalizedbarycentric rational interpolation, we construct Barycentric-Thiele type blendingrational interpolation. Properties of the blending rational interpolation are presendedsuch as characteristic and poles in the interpolation interval, And the error estimates aregiven. numerical examples will be the focus of Barycentric-Thiele type blending rationalinterpolation、 Thiele type continued fraction interpolation and barycentric rationalinterpolation of the three comparison,these numerical examples are presented to verifythe correctness and validity of this method.3As Thiele type continued fraction interpolation and barycentric rationalinterpolation are framework,we construct Triple Barycentric-Thiele type blendingrational interpolation. Properties of the blending rational interpolation are presendedsuch as characteristic and poles in the interpolation interval. Numerical simulationresults show that, the interpolation method has better approximating effect.