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

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

Herbert J. Bernstein

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Description: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 left to preserve the state of such historical works.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with An Accelerated Bisection Method for the Calculation of Eigenvalues of a Symmetric Tridiagonal Matrix (Classic Reprint). To get started finding An Accelerated Bisection Method for the Calculation of Eigenvalues of a Symmetric Tridiagonal Matrix (Classic Reprint), you are right to find our website which has a comprehensive collection of manuals listed.
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Description: 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 left to preserve the state of such historical works.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with An Accelerated Bisection Method for the Calculation of Eigenvalues of a Symmetric Tridiagonal Matrix (Classic Reprint). To get started finding An Accelerated Bisection Method for the Calculation of Eigenvalues of a Symmetric Tridiagonal Matrix (Classic Reprint), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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

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

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