The paper has studied nonlinear rational parameterized fitting algorithms with keeping endpoints and gauss interpolation algorithms. Rational continued fraction function got satisfies the interpolation conditions through inverse difference-continued fraction. The two algorithms have property of keeping endpoints, the middle data points chosen is parameterized through minimum error function, these two algorithms have much flexibility in processing data. Experimental results shows that the function values fitted by parameterized rational continued fraction are more accuracy than these fitted by gauss interpolation polynomial. Therefore, the rational continued fraction fitting functions not only preserve endpoints but also the values predicted are more accurate.
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