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Recursive blocked algorithms for linear systems with Kronecker product structure

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Abstract

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of generalized Sylvester matrix equations, as they arise from the discretization of PDEs with separable coefficients or the approximation of certain models in macroeconomics. By combining recursions with a mechanism for merging dimensions, an efficient algorithm is derived that outperforms existing approaches based on Sylvester solvers.

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Acknowledgements

Daniel Kressner sincerely thanks Michael Steinlechner and Christine Tobler for insightful discussions on the algorithms presented in this work and their implementation.

Funding

The work of the first author was financially supported by the National Natural Science Foundation of China (Grant No. 11801513).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310029, Zhejiang, People’s Republic of China

    Minhong Chen

  2. Institute of Mathematics, EPF Lausanne, 1015, Lausanne, Switzerland

    Daniel Kressner

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  1. Minhong Chen
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  2. Daniel Kressner
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Correspondence to Daniel Kressner.

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Chen, M., Kressner, D. Recursive blocked algorithms for linear systems with Kronecker product structure. Numer Algor 84, 1199–1216 (2020). https://doi.org/10.1007/s11075-019-00797-5

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