Iam need to use Sparse SVD for factorization of a very large matrix, I couldn't find any article regarding mathematical implementation of Sparse SVD, How is it different from SVD?
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$\begingroup$ Hello ! This Q/A is about the software Mathematica -- are you sure your question is related to Mathematica and not Mathematics ? $\endgroup$– SektorOct 23, 2015 at 11:44
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$\begingroup$ I'm not quite sure what you mean that you couldn't find any articles about this--both Google web search and Google Scholar produce many useful results. If your question is asking about implementation details in the Mathematica context, please clarify that; otherwise, the question will most likely be closed as off-topic. $\endgroup$– Oleksandr R.Oct 23, 2015 at 11:47
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$\begingroup$ @ Sektor: Oh!, Sorry i wanted to ask question in Mathematics section! $\endgroup$– Shreyas BhatOct 23, 2015 at 11:52
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In languages like Matlab and Octave there is a "svds" which uses "eigs" internally to find the largest or smallest moduli eigenvalues where you can specify how many values you want. I have not used Mathematica so much so I can't say much about it.
To implement sparse eigenvalue or singular value extraction, you can for instance use the power method to find the largest one, then factor it out and find the next largest one and so on. That would be straight forward to implement, although I can not say what octave and matlab ( or mathematica ) would use internally to do this.
Here seems to be a lecture explaining how you can do this. But I bet there are loads of other sources on the net which explain different ways to do it.
answered Oct 23, 2015 at 12:30