Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

A stable, rational QR algorithm for the computation of the eigenvalues of an Hermitian, tridiagonal matrix


Author: Christian H. Reinsch
Journal: Math. Comp. 25 (1971), 591-597
MSC: Primary 65F15
DOI: https://doi.org/10.1090/S0025-5718-1971-0295555-4
MathSciNet review: 0295555
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The most efficient program for finding all the eigenvalues of a symmetric matrix is a combination of the Householder tridiagonalization and the QR algorithm. The latter, if carried out in a natural way, requires 4n additions, 10n multiplications, 2n divisions, and n square roots per iteration (n the order of the matrix). In 1963, Ortega and Kaiser showed that the process can be carried out using no square roots (and saving 7n multiplications). However, their algorithm is unstable and several modifications were suggested to increase its accuracy. We, too, want to give such a modification together with some examples demonstrating the achieved accuracy.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F15

Retrieve articles in all journals with MSC: 65F15


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0295555-4
Keywords: Hermitian matrix, symmetric matrix, tridiagonal matrix, all eigenvalues, QR transformation
Article copyright: © Copyright 1971 American Mathematical Society