The Padé-Type Approximation For Pseudo-Multivariate Functions

For the rational approximation of multivariate functions,this thesis gives a Padé-type approximation for pseudo-multivariate functions.In the researches of the rational approximation of multivariate functions,many outstanding scholars have made the tremendous contribution and got a lot of rational approximation forms of multivariate function,such as:bivariate Padéapproximation, bivariate vector rational interpolation,bivariate Padé-type approximation,bivariate Newton- Padéapproximation,bivariate rational spline interpolation,and so on.However, the above mentioned approximation function is too complicated and the calculation of solving coefficients of the numerator and denominator is very difficult.In order to simplify the calculation of complexity,some scholars have presented other methods,such as:nested multivariate Padéapproximation,multivariate Frobenius-Padéapproximation, and so on.Although the above methods can simplify the calculating complications,the convergence of these approximants at the singular points is not satisfactory.The pseudo-multivariate function is a new concept proposed in recent years.It is a special multivariate function.The well known Appell series and Lauricella functions are just pseudo-multivariate functions.The main results of the this thesis include:based on the characters of pseudo-multivariate functions and the Padé-type approximation of univariate functions,the Padé-type rational approximation of pseudo-multivariate functions is constructed;the properties of the Padé-type approximation of the pseudo-multivariate functions are derived from the properties of univariate Padéapproximation;the error analysis of this method is carried out and the error formulae are obtained in functional form and in complex domain respectively.Numerical examples show that our method can not only simplify the calculations,but also accelerate the convergence of the approximating functions at singular points.