An Accelerated Bisection Method for the Calculation of Eigenvalues of a Symmetric Tridiagonal Matrix (Classic Reprint) - Softcover

Bernstein, Herbert J.

Softcover

ISBN 10: 1332095690 ISBN 13: 9781332095698

Publisher: Forgotten Books, 2024

Synopsis

Excerpt from An Accelerated Bisection Method for the Calculation of Eigenvalues of a Symmetric Tridiagonal Matrix Summary. We present a method for the determination of eigenvalues of a symmetric tridiagonal matrix which combines Givens' Sturn bisection [4, 5] with interpolation, to accelerate convergence in high precision cases. By using an appropriate root of the absolute value of the determinant to derive the interpolation weight, results are obtained which compare favorably with the Barth, Martin, Wilkinson algorithm [1]. Subject Classifications: AMS (MOS): 15A18, 15-04, 65F10; CR: 5.14 1. Introduction When a modest subset of the eigenvalues of a symmetric tridiagonal matrix is required, the most effective technique available is the bisection method presented by Givens [4, 5]. As Wilkinson [6] notes, once an eigenvalue is approximately located, final convergence by interpolation may be more economical than continued bisection. However, in the case of repeated or clustered eigenvalues, interpolation is likely to be more expensive than bisection. Distinguishing the isolated eigenvalues from the repeated ones can often require more code and time than completion of the bisection. Indeed, many obvious techniques for converging to eigenvalues faster than with bisection turn out to take fewer steps, but considerably more time, because so much more has to be done in the inner loop. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally

About this title

About the Author

Bernstein teaches physics at Hampshire College, holds a visiting research position at M.I.T., and is president of ISIS.

Edition details

• Publisher: Forgotten Books
• Publication date: 2024
• ISBN 10: 1332095690
• ISBN 13: 9781332095698
• Binding: Paperback
• Language: English
• Number of pages: 31