Conversions between barycentric, RKFUN, and Newton representations of rational interpolants

Elsworth, Steven and Güttel, Stefan (2017) Conversions between barycentric, RKFUN, and Newton representations of rational interpolants. [MIMS Preprint]

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Abstract

We derive explicit formulas for converting between rational interpolants in barycentric, rational Krylov (RKFUN), and Newton form. We show applications of these conversions when working with rational approximants produced by the AAA algorithm [Y. Nakatsukasa, O. Sète, L. N. Trefethen, arXiv preprint 1612.00337, 2016] within the Rational Krylov Toolbox and for the solution of nonlinear eigenvalue problems.

Item Type:	MIMS Preprint
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Stefan Güttel
Date Deposited:	28 Mar 2018 23:59
Last Modified:	28 Mar 2018 23:59
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2632

Available Versions of this Item

• Conversions between barycentric, RKFUN, and Newton representations of rational interpolants. (deposited 02 Nov 2017 13:15)
  • Conversions between barycentric, RKFUN, and Newton representations of rational interpolants. (deposited 03 Nov 2017 14:15)
    • Conversions between barycentric, RKFUN, and Newton representations of rational interpolants. (deposited 22 Nov 2017 20:56)
      • Conversions between barycentric, RKFUN, and Newton representations of rational interpolants. (deposited 28 Mar 2018 23:59) [Currently Displayed]
        • Conversions between barycentric, RKFUN, and Newton representations of rational interpolants. (deposited 04 Oct 2018 10:49)

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