<p>Even a 4 x 4 correlation matrix is sensitive to errors.  In any case, here are some links that might help:</p>

<p><a href="http://www.oxford-man.ox.ac.uk/documents/papers/2011OMI08_Sheppard.pdf" rel="nofollow">http://www.oxford-man.ox.ac.uk/documents/papers/2011OMI08_Sheppard.pdf</a></p>

<p><a href="http://www.kevinsheppard.com/images/4/47/Chapter8.pdf" rel="nofollow">http://www.kevinsheppard.com/images/4/47/Chapter8.pdf</a></p>

<p><a href="http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.5331v1.pdf" rel="nofollow">http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.5331v1.pdf</a></p>

<p><a href="http://cran.r-project.org/web/packages/tawny/index.html" rel="nofollow">http://cran.r-project.org/web/packages/tawny/index.html</a></p>

<p><a href="http://www.rinfinance.com/RinFinance2009/presentations/yollin_slides.pdf" rel="nofollow">http://www.rinfinance.com/RinFinance2009/presentations/yollin_slides.pdf</a></p>

<p><a href="http://nurometic.com/quantitative-finance/tawny/portfolio-optimization-with-tawny" rel="nofollow">http://nurometic.com/quantitative-finance/tawny/portfolio-optimization-with-tawny</a></p>

<p><a href="http://quantivity.wordpress.com/2011/04/17/minimum-variance-portfolios/" rel="nofollow">http://quantivity.wordpress.com/2011/04/17/minimum-variance-portfolios/</a></p>
Can I break down a large-scale correlation matrix?
<p>the correlation matrix is so large (50000by50000) that it is not efficient in calculating what I want. What I want to do is to break it down to groups and treat each as separate correlation matrices. However, how do I deal with the dependence between those smaller correlation matrices? I have been researching online all day but nothing comes up. There should be some algorithm out there that is related to the approximation of large correlation matrices like this, right?</p>