Specify eigenvector for eigs

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Jack A.M.
Jack A.M. on 22 Aug 2020
Commented: John D'Errico on 24 Aug 2020
Is there a way I can speed up the eigenvalue computation time by feeding the function eigs a "guess" eigenvector? I am dealing with large, sparse matrices such that everytime I run the eigenvalue problem, the eigenvector chosen based on smallest eigenvalue changes slightly compared to the last time. As far as I know, in an iterative method, using some sort of a "guess" as an input would make the code more efficient. So perhaps, using the previous eigenvector as a guess would make the generalized eigenvalue problem more efficient.

Answers (1)

Vladimir Sovkov
Vladimir Sovkov on 22 Aug 2020
Matlab documentation:
'StartVector' — Initial starting vector
random vector (default) | vector
Initial starting vector, specified as the comma-separated pair consisting of 'StartVector' and a numeric vector.
The primary reason to specify a different random starting vector is when you want to control the random number stream used to generate the vector.
Note
eigs selects the starting vectors in a reproducible manner using a private random number stream. Changing the random number seed does not affect the starting vector.
Example: d = eigs(A,k,sigma,'StartVector',randn(m,1)) uses a random starting vector that draws values from the global random number stream.
Data Types: double
  2 Comments
John D'Errico
John D'Errico on 24 Aug 2020
It did not speed anything up, because that is not the purpose of being able to provide a starting vector. It should not help.

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