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Lanczos Eigenvectors

  1. Nov 3, 2009 #1
    Hi, I'm applying the Lanczos algorithm to find the minimal eigenvalue of some huge matrix. Now that I've got it I'm trying to find the eigenvector corresponding to this eigenvalue. Now I have looked through book after book after book and I have yet to find an explanation of how to do this that is even the slightest bit approachable and I don't have the time or patience to read through a whole 300 page textbook to understand the authors notations and terminology well enough to glean a probably 10 line algorithm to generate these things. So i'm wondering if someone could simply tell me a bare-bones algorithm or point me to one that accomplishes this (an algorithm not a linear algebra proof from willoughby and callum or some such).

    I have a lanczos algorithm that uses two vectors and the standard lanczos algorithm (http://en.wikipedia.org/wiki/Lanczos_algorithm#The_algorithm). I cannot store more than 2 (maybe 3) vectors (so I can't have something like V=[v1,v2,....,vm]). I generate my tridiagonal lanczos matrix Tm, I can solve for the eigenvalue I want now what do I do? Any help is greatly appreciated, this is driving me mad. It's amazing how many books/internet sources "discuss" this but other then a 5 page linear algebra proof fail to provide any clear explanation, much less an algorithm or an example.
     
  2. jcsd
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