Is there any special technique to find the SVD for a square, symmetric, 3x3 matrix?
The only technique I know is to find the eigenvalues and eigenvectors. The singular value decomposition of the square matrix A is the factorisation $\displaystyle A=P^{\,\textsc{t}}DP$, where D is the diagonal matrix whose entries are the eigenvalues of A, and P is the orthogonal matrix whose columns are the corresponding normalised eigenvectors.