Homotopy method for the eigenvalues of symmetric tridiagonal matrices

Philip Brockman; Timothy Carson; Yun Cheng; T. M. Elgindi; K. Jensen; X. Zhoun; M. B.M. Elgindi

doi:10.1016/j.cam.2012.08.010

Homotopy method for the eigenvalues of symmetric tridiagonal matrices

Philip Brockman, Timothy Carson, Yun Cheng, T. M. Elgindi, K. Jensen, X. Zhoun, M. B.M. Elgindi

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We will present the homotopy method for finding eigenvalues of symmetric, tridiagonal matrices. This method finds eigenvalues separately, which can be a large advantage on systems with parallel processors. We will introduce the method and establish some bounds that justify the use of Newton's method in constructing the homotopy curves.

Original language	English (US)
Pages (from-to)	644-653
Number of pages	10
Journal	Journal of Computational and Applied Mathematics
Volume	237
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2012.08.010
State	Published - Jan 1 2013

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

Keywords

Eigenvalue
Homotopy
Newton-Kantorovich Theorem
Symmetric
Tridiagonal

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10.1016/j.cam.2012.08.010

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title = "Homotopy method for the eigenvalues of symmetric tridiagonal matrices",

abstract = "We will present the homotopy method for finding eigenvalues of symmetric, tridiagonal matrices. This method finds eigenvalues separately, which can be a large advantage on systems with parallel processors. We will introduce the method and establish some bounds that justify the use of Newton's method in constructing the homotopy curves.",

keywords = "Eigenvalue, Homotopy, Newton-Kantorovich Theorem, Symmetric, Tridiagonal",

author = "Philip Brockman and Timothy Carson and Yun Cheng and Elgindi, {T. M.} and K. Jensen and X. Zhoun and Elgindi, {M. B.M.}",

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AU - Brockman, Philip

AU - Carson, Timothy

AU - Cheng, Yun

AU - Elgindi, T. M.

AU - Jensen, K.

AU - Zhoun, X.

AU - Elgindi, M. B.M.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We will present the homotopy method for finding eigenvalues of symmetric, tridiagonal matrices. This method finds eigenvalues separately, which can be a large advantage on systems with parallel processors. We will introduce the method and establish some bounds that justify the use of Newton's method in constructing the homotopy curves.

AB - We will present the homotopy method for finding eigenvalues of symmetric, tridiagonal matrices. This method finds eigenvalues separately, which can be a large advantage on systems with parallel processors. We will introduce the method and establish some bounds that justify the use of Newton's method in constructing the homotopy curves.

KW - Eigenvalue

KW - Homotopy

KW - Newton-Kantorovich Theorem

KW - Symmetric

KW - Tridiagonal

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Homotopy method for the eigenvalues of symmetric tridiagonal matrices

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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