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