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.