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Multiple orthogonal polynomials applied to matrix function evaluation

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Abstract

Multiple orthogonal polynomials generalize standard orthogonal polynomials by requiring orthogonality with respect to several inner products. This paper discusses an application to the approximation of matrix functions and presents quadrature rules that generalize the anti-Gauss rules proposed by Laurie.

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Acknowledgements

The authors would like to thank Ulises Fidalgo and Qiang Ye for valuable discussions, and the referees for comments. The research was supported in part by NSF grants DMS-1720259 and DMS-1729509.

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Authors and Affiliations

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

    Hessah Alqahtani

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

    Hessah Alqahtani & Lothar Reichel

Authors
  1. Hessah Alqahtani
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  2. Lothar Reichel
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Correspondence to Lothar Reichel.

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Communicated by Marko Huhtanen.

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Alqahtani, H., Reichel, L. Multiple orthogonal polynomials applied to matrix function evaluation. Bit Numer Math 58, 835–849 (2018). https://doi.org/10.1007/s10543-018-0709-x

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  • DOI: https://doi.org/10.1007/s10543-018-0709-x

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