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linear-algebralapackblas
Robert T. McGibbon
Robert T. McGibbon

Reputation: 5287

Warm starting symmetric eigenvalue computation?

Do any standard (LAPACK / ARPACK / etc) implementations of the symmetric eigenvalue problem allow "warm starting"? That is, can they be accelerated if I already have a pretty good guess for the eigenvalues and eigenvectors of my matrix.

With Rayleigh quotient iteration or power iteration, this should be pretty obvious, but I don't see how to do this with standard eigensolver software. I'd prefer not to write my own eigensolver.

Upvotes: 0

Views: 131

Answers (1)

ztik
ztik

Reputation: 3612

What you need is an iterative eigenvalue solve algorithm.

  • LAPACK uses a direct eigensolver and having an estimation of eigenvectors is of no use. There is a QR iterative refinement in its routines. However It requires Hessenberg matrices. I do not think you could use these routines.
  • You could use ARPACK library, specify the starting vector a set info argument equal to one.
  • Also I suggest to reconsider writing your own QR solver. It is very simple.

A basic QR implementation using lapack could be:

Initialize Q, A
repeat
  QR = A (dgeqrf)
  A = RQ (dormqr)
until convergence (dnrm2)

Upvotes: 2

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