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I have a very big matrix assume $1000 \times 1000$. I want to find $k$ of its algebraically smallest eigenvalues where $k$ is $2$ or $3$.

I am using MATLAB to solve this problem.

My Try:

  1. I try to use power method. I wrote my own code but due to some numerical precision error it is not working.
  2. I use MATLAB's in build eigs function, but when my eigenvalues are very small (in the order of $10^{-5}$), it started malfunctioning.

Looking forward for any generous suggestion. Also, if you know any open source tested power method MATLAB code, then please let me know about it. Thanks.

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