The Godunov-Inverse Iteration : A fast and accurate solution to the symmetric tridiagonal eigenvalue problem.

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We present a new hybrid algorithm based on Godunov's method for computing eigenvectors of symmetric tridiagonal matrices and Inverse Iteration, which we call the Godunov-Inverse Iteration Algorithm. We use eigenvectors computed according to Godunov's method as starting vectors in the Inverse Iteration, replacing any nonnumeric elements of the Godunov eigenvectors with random uniform numbers. We use the right-hand bounds of the Ritz intervals found by the bisection method as Inverse Iteration shifts, while staying within guaranteed error bounds. In most test cases convergence is reached after only one step of the iteration, producing error estimates that are as good as ... continued below

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13 p.

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Matsekh, A. M. (Anna M.) November 27, 2002.

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We present a new hybrid algorithm based on Godunov's method for computing eigenvectors of symmetric tridiagonal matrices and Inverse Iteration, which we call the Godunov-Inverse Iteration Algorithm. We use eigenvectors computed according to Godunov's method as starting vectors in the Inverse Iteration, replacing any nonnumeric elements of the Godunov eigenvectors with random uniform numbers. We use the right-hand bounds of the Ritz intervals found by the bisection method as Inverse Iteration shifts, while staying within guaranteed error bounds. In most test cases convergence is reached after only one step of the iteration, producing error estimates that are as good as or superior to those produced by standard Inverse Iteration implementations.

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13 p.

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  • Submitted to: Sixth IMACS international symposium on iterative methods in scientific computing, March 27-30, 2003 University of Colorado at Denver

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  • Report No.: LA-UR-02-7561
  • Grant Number: none
  • Office of Scientific & Technical Information Report Number: 976481
  • Archival Resource Key: ark:/67531/metadc926775

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  • November 27, 2002

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 9, 2016, 11:39 p.m.

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Matsekh, A. M. (Anna M.). The Godunov-Inverse Iteration : A fast and accurate solution to the symmetric tridiagonal eigenvalue problem., article, November 27, 2002; United States. (digital.library.unt.edu/ark:/67531/metadc926775/: accessed June 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.