Report Number: CS-TR-66-41
Institution: Stanford University, Department of Computer Science
Title: Accurate eigenvalues of a symmetric tri-diagonal matrix
Author: Kahan, William
Date: July 1966
Abstract: Having established tight bounds for the quotient of two different lub-norms of the same tri-diagonal matrix J, the author observes that these bounds could be of use in an error-analysis provided a suitable algorithm were found. Such an algorithm is exhibited, and its errors are thoroughly accounted for, including the effects of scaling, over/underflow and roundoff. A typical result is that, on a computer using rounded floating point binary arithmetic, the biggest eigenvalue of J can be computed easily to within 2.5 units in its last place, and the smaller eigenvalues will suffer absolute errors which are no larger. These results are somewhat stronger than had been known before.