ELA, Volume 16, pp. 99-110, March 2007, abstract.

Using Least-Squares to Find an Approximate Eigenvector

David Hecker and Deborah Lurie

The least-squares method can be used to approximate an 
eigenvector for a matrix when only an approximation is 
known for the corresponding eigenvalue. In this paper, 
this technique is analyzed and error estimates are 
established proving that if the error in the eigenvalue 
is sufficiently small, then the error in the approximate 
eigenvector produced by the least-squares method is also 
small. Also reported are some empirical results based 
on using the algorithm.