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I would like to know how to unroll loop-carried dependency inside the cholesky algorithm. What are the techniques that I should know to accomplish this work? I need to know it because I want to parallelize it. I was reading about from the following link: http://cnx.org/content/m32782/latest/, Should I to pay attention to that page? Is the last correct?

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The link is correct. To parallelize an algorithm, you have to handle its dependencies. However, this is not a trivial task, even if you know this.

There are plenty of articles to be found on how to parallelize Cholesky (just google for "parallel Cholesky"). If you do not have experience in parallelizing algorithms, then I would highly recommend to simply implement one of those algorithms, or to use a library that can do so. When you implement it yourself, you will for sure not come up with a good solution.

Examples of articles:

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  • $\begingroup$ I don't have any experience about parallelizing algorithms, so... do you think I should implement an algorithm from internet? Any recommendation about starting parallelizing algorithms? $\endgroup$ – facunvd Nov 8 '12 at 10:07

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