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A Krylov Subspace Method for the Approximation of Bivariate Matrix Functions

  • Daniel KressnerEmail author
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 30)

Abstract

Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fréchet derivative. In this work, we propose a novel tensorized Krylov subspace method for approximating such bivariate matrix functions and analyze its convergence. While this method is already known for some instances, our analysis appears to result in new convergence estimates and insights for all but one instance, Sylvester matrix equations.

Keywords

Matrix function Krylov subspace method Bivariate polynomial Fréchet derivative Sylvester equation 

Notes

Acknowledgements

The author thanks Marcel Schweitzer for inspiring discussions on the topic of this work and Christian Lubich for the idea of the proof for Lemma 5. He also thanks the referees for their constructive comments, which improved the presentation of the paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of MathematicsEPF LausanneLausanneSwitzerland

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