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

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Abstract

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.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Notes

  1. This work won the very first PhD thesis prize at the Householder meeting (then called the Gatlinburg conference)

  2. In the commun notation used in the litterature, the parameter \(\mu\) is replaced by \(\nu\).

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Acknowledgements

The paper has benefitted from a careful reading from an anonymous referee who made a number of suggestions and pointed out two references on related work.

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  1. Computer Science & Engineering, University of Minnesota, Twin Cities, USA

    Yousef Saad

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Correspondence to Yousef Saad.

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The author declares that he has no conflict of interest.

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

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Saad, Y. Revisiting the (block) Jacobi subspace rotation method for the symmetric eigenvalue problem. Numer Algor 92, 917–944 (2023). https://doi.org/10.1007/s11075-022-01377-w

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