Can we do SVD without computing eigenvector decomposition?

Question

I'am studying SVD and PCA.(via Andrew Ng's coursera class)

I heard that using SVD for PCA is numerically more stable than doing eigenvector decomposition to covariance matrix.

From my knowledge so far, I have to do eigenvector decomposition to do SVD.

If he is not wrong, it seems that there is a way to calculate [U, sigma, V] without doing eigenvector decomposition to covariance matrix.

Is there a way? or is my understanding wrong?

Answer 1

Yes, there are stable ways to so it without computing the eigenvalue decomposition. See here for a discussion.

You can also see discussions in Trefethen & Bau as well as Golub & van Loan.