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In this paper, we show that the SVD of a matrix can be constructedefficiently in a hierarchical approach. Our algorithm is proven to recover thesingular 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 alsoshow that the proposed method is stable with respect to roundoff errors orcorruption of the original matrix entries. Numerical experiments validate theproposed algorithms and parallel cost analysis.

A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks