A Parameter Estimation Method Of Rational Function Approximation

In the past few years, when people want to fnd the relationship between twovariables, they usually use a large number of experiments to observe the data, andthen use the software to draw a picture of the data. From the picture we hope to fndsome rules and then we can use the corresponding model. For example, if the pointsof the graph is substantially in a straight line, and the deviation on some small,then we consider the use of linear model. When we can not fnd the rule, we usuallyuse the polynomial approximation. And then when the polynomial approximationefect is not good, we can use the rational function approximation.While the efect of the rational function approximation is good, the parameterestimation is very hard. In this paper, I present a approximate method for solvingthe regression parameter of the rational function approximation, using the thoughtof the rational function interpolation to make the nonlinear problem into a linearproblem. When approximatively estimate the parameters, and then substitute themto the residual sum of squares, and compared with the polynomial approximation,we obtained a satisfactory results: the rational function is better than the poly-nomial approximation under the same times, the residual sum of squares is small.Moreover, faster than directly solving for the parameters of the rational functionapproximation. So, this method is efcacious.From the the numerical test given in this paper, we can be sure that this methodcan approximatively determine the regression parameter of the rational functionapproximation, and makes the residual sum of squares can reach very small value.