The block rational Arnoldi method

Elsworth, Steven and Güttel, Stefan (2019) The block rational Arnoldi method. [MIMS Preprint]

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The block version of the rational Arnoldi method is a widely used procedure for generating an orthonormal basis of a block rational Krylov space. We study block rational Arnoldi decompositions associated with this method and prove an implicit Q theorem. We relate these decompositions to nonlinear eigenvalue problems. We show how to choose parameters to prevent a premature breakdown of the method and improve its numerical stability. We explain how rational matrix-valued functions are encoded in rational Arnoldi decompositions and how they can be evaluated numerically. Two different types of deflation strategies are discussed. Numerical illustrations using the MATLAB Rational Krylov Toolbox are included.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Stefan Güttel
Date Deposited: 17 Feb 2019 07:36
Last Modified: 17 Feb 2019 07:36

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