# Lanczos Eigenvectors

maverick_starstrider
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.

## Answers and Replies

omephy
Did you solve this issue eventually?