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Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix

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Abstract

This paper is concerned with the approximation of matrix functionals of the form wTf(A)v, where \(A\in \mathbb {R}^{n\times n}\) is a large nonsymmetric matrix, \(\boldsymbol {w},\boldsymbol {v}\in \mathbb {R}^{n}\), and f is a function such that f(A) is well defined. We derive Gauss–Laurent quadrature rules for the approximation of these functionals, and also develop associated anti-Gauss–Laurent quadrature rules that allow us to estimate the quadrature error of the Gauss–Laurent rule. Computed examples illustrate the performance of the quadrature rules described.

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Acknowledgements

The authors would like to thank a referee for carefully reading the manuscript and for comments that lead an improved presentation. This work was begun while L.R. visited the University of Banja Luka. He would like to thank M.P. for making this visit possible and enjoyable.

Funding

H.A. was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant no. G-111-665-1441. L.R. was supported by NSF grant DMS-1729509.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA

    J. Alahmadi & L. Reichel

  2. Department of Mathematics, Faculty of Science and Arts, King Abdulaziz University, Rabigh, Saudi Arabia

    H. Alqahtani

  3. Department of Mathematics and Informatics, Faculty of Science, University of Banja Luka, M. Stojanovića 2, 51000, Banja Luka, Bosnia and Herzegovina

    M. S. Pranić

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  1. J. Alahmadi
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  2. H. Alqahtani
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  3. M. S. Pranić
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  4. L. Reichel
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Correspondence to J. Alahmadi.

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Alahmadi, J., Alqahtani, H., Pranić, M.S. et al. Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix. Numer Algor 88, 1937–1964 (2021). https://doi.org/10.1007/s11075-021-01101-0

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  • DOI: https://doi.org/10.1007/s11075-021-01101-0

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