The Yule-Walker equations resulting from [[minimizing the energy of the residue]] can be solved with any matrix inversion package.
$
\mathbf{a} = \mathbf{R}^{-1} \mathbf{\gamma}
$
However, due to the special form of matrix $\mathbf{R}$ some efficient solutions are possible.
The first one is called the covariance method and is derived by limiting the interval where the squared error summation takes place:
$
\mathcal{E} = \sum_{n=0}^{N-1} \left( s(n) - \sum_{k=1}^{P} a_k s(n-k) \right)^2
$
The second efficient solution is the [[autocorrelation method]] that assumes that the signal $s(n)$ is zero outside an interval of $N$ samples. This assumes the [[windowing]] of the signal.