Updating the singular value decomposition
The method uses Fast Multipole Method (FMM) for updating singular vectors in $O(n \ \text (\frac))$ time, where $\epsilon$ is the precision of computation.
Highlights of version 6.20 Version 6.20 brings lots of new functionality especially with regards to system testing.
" from the Computational Science SE gives a number of MATLAB and C implementations that you may want to consider. implementation are wrappers around C, C or FORTRAN implementations.
An efficient Singular Value Decomposition (SVD) algorithm is an important tool for distributed and streaming computation in big data problems.
For this package to work only Numpy, Scipy and Matplotlib are required. However, Scipy need to be compiled from sources in order to use some LAPACK function "dlasd4" which are not exposed originally.
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It is observed that update of singular vectors of a rank-1 perturbed matrix is similar to a Cauchy matrix-vector product.
With this observation, in this paper, we present an efficient method for updating Singular Value Decomposition of rank-1 perturbed matrix in $O(n^2 \ \text(\frac))$ time.
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The basic of this update are dictated by the Sherman-Morrison formula.. \begin A^* = A - UV^T \end the Woodbury formula comes into play.