Revisiting the (block) Jacobi subspace rotation method for the symmetric eigenvalue problem

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The paper revisits the topic of block-Jacobi algorithms for the symmetric eigenvalue problem by proposing a few alternative versions. The main advantage of a block Jacobi method is that it is built entirely from computations with small dense matrices. The proposed mehod is based on a sequence of subspace rotations whose determination requires to solve small Riccati-like correction equation. The paper discusses theoretical and algorithmic aspects of the algorithm, and illustrates its behavior on a few simple examples.

Original languageEnglish (US)
Pages (from-to)917-944
Number of pages28
JournalNumerical Algorithms
Issue number1
StatePublished - Jan 2023

Bibliographical note

Funding Information:
This work was supported by NSF under grant DMS-2011324.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Jacobi algorithm
  • Riccati equations
  • Symmetric eigenvalue problem


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