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How to calculate the polynomial coefficients of any arbitrary polynomial to fit data

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How to calculate the polynomial coefficients of any arbitrary polynomial to fit data

Posted August 1, 2016 at 08:06 by Tobi

Dear all,

if you are interested in the calculation of polynomial coefficients to fit some data, you can check the method of least squares on my homepage. Here I explained everything in detail and also gave an example how to build the matrix A and the solution vector b for the problem we are discussing there. The polynomial that I am using in the example is:

\ln(\mu) = A + B \ln(T) + C\ln(T)^2 + D \ln(T)^3

How to build the matrix A and the solution vector b is explained there. Doing this, we end up with a squared matrix the same rank as the two vectors b and x. Hence we can simply find the polynomial coefficients A, B, C and D by solving the following equation:

\textbf{x} = \textbf{b} \bullet \textbf{A}^{-1}

The only difficulty is to calculate the inverse of A (that is in fact really easy by using some Gauss elimination).

http://www.holzmann-cfd.de/index.php...omcoefficients
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