Report Number: CS-TR-66-42
Institution: Stanford University, Department of Computer Science
Title: When to neglect off-diagonal elements of symmetric
tri-diagonal matrices
Author: Kahan, William
Date: July 1966
Abstract: Given a tolerance $\epsilon$ > 0, we seek a criterion by
which an off-diagonal element of the symmetric tri-diagonal
matrix J may be deleted without changing any eigenvalue of J
by more than $\epsilon$. The criterion obtained here permits
the deletion of elements of order $\sqrt{\epsilon }$ under
favorable circumstances, without requiring any prior
knowledge about the separation between the eigenvalues of J.
http://i.stanford.edu/pub/cstr/reports/cs/tr/66/42/CS-TR-66-42.pdf