The algorithm to compute SVD of a matrix $A$ is as the following,
- Compute an orthogonal basis $Q$ for the range of $A$.
- Do singular value decomposition on matrix $B=Q^TA$.
- Let $B_k$ be the rank-$k$ truncated SVD of $B$, return $QB_k$.
Is there any name for this algorithm, can anyone help provide some reference? Why we don't directly compute lower-rank approximation by SVD on $A$? Is this for the reason of numerical stability? Thanks!