Divide by zero

Do you already know that your function y6 is wrong because you used the wrong value (0) for x[N in your routine X_Gauss()? You have compared to y(x) (the result obtained with lsolve) yourself and must have seen that those two functions are far apart.

See my remarks here http://communities.ptc.com/message/265948#265948

Your new problem may be due to the fact that you try to solve a system consisting of still seven equations but with just six variables, as you are just searching for a polynomial of order 5 now.

lsolve will still handle that kind of systems which are not square, too, but the result may not be satisfactory as the system may not have a solution anyway. So its no surprise that you run into problems using your self made Gauss elimination routines.

Normally you won't be able to find a polynomial of fifth order which runs through seven given points - the best you could get is a close approximation and thats called regression. Is it this you are after? lsolve will get you an approximation here but by far not the best one you can get with a 5th order polynomial. Mathcad has other means to obtain that kind of fits.

Here you have your original data and the results of the sixth and fifth order polynomila compared to each other.

In the plot the difference is hardly seen unless you zoom in.