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POHow do I obtain the eigenvalues of a huge matrix (size: 2x10^5)
 

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  1. POHow do I obtain the eigenvalues of a huge matrix (size: 2x10^5)
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    1. COIn double precision just storing the dense 200000x200000 matrix will be ~300GB of memory. The problem is most likely not the programming language that you use, but the RAM and swap space of the computer you are using.
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      1. POHow do I obtain the eigenvalues of a huge matrix (size: 2x10^5)
      1. USChris Johnson
    2. CODo you know the nature of your matrix? If it's a random Gaussian matrix (or if you can approximate your data to be so), there are several analytical results I could provide that will tell you the distribution of the eigenvalues (asymptotically). For a matrix of this size, you almost _cannot_ go wrong if you use the asymptotic results, and I'd dare to wager that a 200000 point sample from that distribution will be pretty damn near the actual eigenvalues. If this is not the case, do you know if your requirements are small? Like for e.g., do you need just the largest eigenvalue or all?
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    3. COFurther along yoda's line of thought: if you're doing stats work (which includes a lot of what is called data mining and machine learning), do you really need to work with the full data set or would a smaller (~1e4) sample be sufficient? You might consider providing some details about the problem that is behind this matrix, there might be better ways of getting what you're after.
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      1. USmu is too short
 

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