# Low rank Matrix factorization

Hello,

I've a SPD matrix A; which needs to be factorized as ${A=SS^{T}}$. But, using Cholesky for this purpose is prohibitive in terms of computational cost. Moreover, matrix is Dense and has a slow decaying eigen-spectrum.

Can anything be suggested for replacement of cholesky. Moreover, it need not be exact,anything approximate will work as long as $y=Sz$ and the quantity $y^{T}y$ is what I'm trying to preserve.($z$ is standard normal vector)

Thanks

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Why do you say "low rank"? –  Igor Rivin Mar 27 '12 at 1:31
Right now I'm trying using truncated SVD; (In general it need not be low rank) Sorry about the confusion –  zimbra314 Mar 28 '12 at 4:55