Binary Mixed Rational Interpolation Method And Its Calculation

Interpolation is one of the core tools of mathematics.The solution of interpolation problem is to get some values from complex functions and use a simple interpolation function to replace the original function.Interpolation is widely used in data processing of engineering technology and control field,and interpolation is the basis of numerical approximation,such as numerical differentiation and integration,approximate calculation of function value.The models of most problems in science and life are often nonlinear problems.Rational interpolation function is a typical nonlinear approximation method.With the emergence and development of computer,the theoretical and applied research of rational approximation has attracted more and more attention.There are many ways to construct rational interpolation functions.Polynomial interpolation is simple and easy to construct,but it can't avoid the unreachable points and has a large amount of calculation.Continued fraction interpolation has strong recursion,but it can't avoid poles and other shortcomings.Barycentric rational interpolation can avoid these problems,so in practice,the above interpolation methods are nested appropriately to obtain the required rational interpolation function.Based on Stieltjes symmetric continued fractions,Newton polynomials and generalized Barycentric rational interpolation,this paper constructs binary rational interpolation functions of different nested types on different grid points by defining appropriate mixed deficit quotient algorithms.First,the binary Stieltjes-Newton rational interpolation is constructed on the lower triangular mesh,then the binary Barycentric-Newton rational interpolation is constructed on the rectangular mesh,and finally,the binary generalized Barycentric-Stieltjes-Newton rational interpolation is constructed on the upper triangular mesh.Three kinds of interpolation algorithms are proved to satisfy the given interpolation conditions and the properties of interpolation functions are also studied.Through the discrete numerical example,the feasibility and effectiveness of the interpolation algorithm are verified.Then through the continuous function example,the interpolation function images under different algorithms are obtained with the help of computer software drawing.The advantages and disadvantages of the interpolation algorithm in this paper are compared and analyzed.