User has to enter total number N of points for approximation. It is convenient to store the data in a file when one has a large number of points. It should be the text file (with .txt extension), which contains exactly 2N numbers separated by white space or new line ("Enter"). Note that two integer numbers without separator will be read as one number, for example "23" and "67" will be read as "2367". Two float numbers without separator could be corrupted, for example "0.34" and "3.5" typed as "0.343.5" can be read as "0.343" and "0.5". We check the format of input numbers and in the most cases one will get an error message if the format is not valid, but it is the responsibility of the user to prepare the input data properly. First N numbers should correspond to x-coordinates of given points and the second set of N numbers should correspond to y-coordinates. User can arrange them in any order, but first x-coordinate (first point) should correspond to first y-coordinate etc. One can use "Browse" to select the required file and click "Upload" to submit.

On the next page user should enter three parameters of approximation, which allow to govern the process of calculation and to reach required accuracy. The first is the maximum number of coefficients of Pade approximation. The program calculates and chooses the best approximation by increasing this number from 3 until the maximum entered by user will be reached. The second parameter is the maximum value of correlation coefficient of data fitting. The third one is the required accuracy of approximation. All these values will be printed back with the result of calculation. The calculation will be completed if one of the following 3 conditions is reached:

  1. The correlation coefficient is equal to or greater than that entered by user.
  2. The accuracy of approximation is equal to or less than that entered by user. The accuracy of approximation is calculated as the ratio of the maximum error of approximation to the mean value of absolute values of ordinates of all given points.
  3. The current amount of coefficients of the approximation function is equal to the maximum entered by user (but not greater than the number of given points).

If the first condition is not important, user can enter "1" for the correlation coefficient. If the second condition is not crucial, user can enter the allowed minimum (0.01) for the accuracy of approximation. In this case, the calculation will probably be completed when the entered number of coefficients of the approximation function will be reached. At each calculation one will get and can print the approximation formula, the table of given data and their approximation, the calculated correlation coefficient and the accuracy of approximation. After analyzing the result, you can correct the input of governing parameters of approximation to get the desired result. We also show "The number of iterations without significant changing of correlation coefficient", which means that the change of correlation coefficient did not exceed 0.001 at last iterations. In this case user can try to reduce the number of coefficients of the approximation function without loss of accuracy.