Homotopy method for the eigenvalues of symmetric tridiagonal matrices

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)644-653
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume237
Issue number1
DOIs
Publication statusPublished - 1 Jan 2013

Fingerprint

Homotopy Method
Tridiagonal matrix
Newton-Raphson method
Symmetric matrix
Eigenvalue
Parallel Processors
Newton Methods
Justify
Homotopy
Curve

Keywords

  • Eigenvalue
  • Homotopy
  • Newton-Kantorovich Theorem
  • Symmetric
  • Tridiagonal

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Homotopy method for the eigenvalues of symmetric tridiagonal matrices. / Brockman, Philip; Carson, Timothy; Cheng, Yun; Elgindi, T. M.; Jensen, K.; Zhoun, X.; Elgindi, Mohamed.

In: Journal of Computational and Applied Mathematics, Vol. 237, No. 1, 01.01.2013, p. 644-653.

Research output: Contribution to journalArticle

Brockman, Philip ; Carson, Timothy ; Cheng, Yun ; Elgindi, T. M. ; Jensen, K. ; Zhoun, X. ; Elgindi, Mohamed. / Homotopy method for the eigenvalues of symmetric tridiagonal matrices. In: Journal of Computational and Applied Mathematics. 2013 ; Vol. 237, No. 1. pp. 644-653.
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