4

Given a large symmetric matrix $A$, there are methods to find the largest or smaller eigenvalue, or the eigenvalue closest to some initial value.

Is there any method to find the normalized eigenvector with maximum overlap (dot product) with an initial vector?

Jellby
  • 247
  • 1
  • 12
  • The question doesn't quite make sense. If $v$ is an eigenvector, then so are $2v$ and $3v$ and $10000000000000000000000v$ and so on, so the dot product with the initial vector is unbounded; there is no maximum. – Gerry Myerson Feb 27 '14 at 10:11
  • 1
    @GerryMyerson one could consider normalised eigenvectors, obviously. – Algebraic Pavel Feb 27 '14 at 10:15
  • I knew I was forgetting something, I fixed the question. – Jellby Feb 27 '14 at 10:48
  • Please see https://scicomp.stackexchange.com/questions/28111/eigenvector-with-maximum-overlap/30528#30528 for the solution! – as2457 Jan 31 '19 at 08:08

0 Answers0