  In this paper, we show that the SVD of a matrix can be constructed
efficiently in a hierarchical approach. Our algorithm is proven to recover the
singular values and left singular vectors if the rank of the input matrix $A$
is known. Further, the hierarchical algorithm can be used to recover the $d$
largest singular values and left singular vectors with bounded error. We also
show that the proposed method is stable with respect to roundoff errors or
corruption of the original matrix entries. Numerical experiments validate the
proposed algorithms and parallel cost analysis.
