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Can someone give me a bit more information about what mathematical method Mathematica is using, (preconditioner, filtering-restarting, deflation) in the Lanczos implementation when I input something like this:

{eig, eivec} = 
 Eigensystem[
  SparseArray[(Heff + ConjugateTranspose[Heff])/2], -1, 
  Method -> {"Arnoldi", "StartingVector" -> startvec, 
    "Tolerance" -> tolerance, "MaxIterations" -> iterations}]`

I want to always compute single eigenvalue with the smallest magnitude.

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    $\begingroup$ The implementation of the Arnoldi method uses the ARPACK library. $\endgroup$ – ilian Jan 7 '16 at 15:36
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Quoting a comment by @ilian:

The implementation of the Arnoldi method uses the ARPACK library.

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