Homotopy method for the eigenvalues of symmetric tridiagonal matrices

  • Authors:

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

  • Affiliations:

  • University of North Dakota, United States;Carnegie Mellon University, United States;University of Virginia, United States;Courant Institute of Mathematical Sciences, NYU, United States;Dickenson University, United States;University of Wisconsin-Eau Claire, United States;Texas A&M University, Qatar

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2013

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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.