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An efficient Singular Value Decomposition (SVD) algorithm is an importanttool for distributed and streaming computation in big data problems. It isobserved that update of singular vectors of a rank-1 perturbed matrix issimilar to a Cauchy matrix-vector product. With this observation, in thispaper, we present an efficient method for updating Singular Value Decompositionof rank-1 perturbed matrix in $O(n^2 \ \text{log}(\frac{1}{\epsilon}))$ time.The method uses Fast Multipole Method (FMM) for updating singular vectors in$O(n \ \text{log} (\frac{1}{\epsilon}))$ time, where $\epsilon$ is theprecision of computation.

Updating Singular Value Decomposition for Rank One Matrix Perturbation