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.