I do have to evaluate a property defined as
$$w = \sqrt{\det\left(\textbf{J}\,\textbf{J}^\text{T}\right)} = \prod_{i = 1}^n \sigma_i,$$
where $\textbf{J} \in R^{3 x n}$ and $n>3$.
Using the Jacobi-SVD, from my understanding, the complexity should be $O\left(3^2\,n\right)$, which also accounts for the complexity of the matrix product (unless I messed it up).
Thus I guess that using the SVD will require less calculations will consume less time. Can you back up my decision or are my derivations incorrect.