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

Herbert J. Bernstein

Hardcover

ISBN 10: 0483850160 ISBN 13: 9780483850163

Publisher: Forgotten Books, 2018

Synopsis

Efficiently find all eigenvalues of a real symmetric tridiagonal matrix with a proven, adaptive approach.

This work presents an accelerated Sturm bisection method that enhances the classic technique by using interpolation and adaptive updates to converge faster.

The description explains how to count eigenvalues with sign observations, avoid costly rescalings, and incorporate adaptive parameters to handle well-isolated and clustered eigenvalues. It also discusses practical implementation issues, including handling determinants, rescaling, and tabulating results for specific hardware.

• Introduces an accelerated bisection approach for tridiagonal matrices and explains how interpolation can speed convergence.
• Discusses how to count eigenvalues using sign changes and how to handle potential numerical issues like underflow and overflow.
• Details adaptive strategies for updating division points and a practical FORTRAN routine tailored to existing workflows.
• Offers test results showing improvements in iteration counts versus prior methods.

Ideal for readers working with numerical linear algebra who need faster eigenvalue computations for symmetric tridiagonal systems, especially when high precision is required.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0483850160
• ISBN 13: 9780483850163
• Binding: Hardcover
• Number of pages: 29