Rational Krylov for eigenvalue computation and model order reduction

DOI10.1007/s10543-006-0085-9zbMath1105.65036OpenAlexW2049015219MaRDI QIDQ857552

K. Henrik A. Olsson, Axel Ruhe

Publication date: 19 December 2006

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-006-0085-9

zbMATH Keywords

numerical examplesArnoldi decompositionrational Krylov algorithmshift-and-invert spectral transformation

Mathematics Subject Classification ID

Related Items (12)

A global rational Arnoldi method for model reduction ⋮ Review and assessment of interpolatory model order reduction methods for frequency response structural dynamics and acoustics problems ⋮ An adaptive scheme for a class of interpolatory model reduction methods for frequency response problems ⋮ Adaptive rational Krylov subspaces for large-scale dynamical systems ⋮ Strategies for spectrum slicing based on restarted Lanczos methods ⋮ Refined isogeometric analysis for generalized Hermitian eigenproblems ⋮ On convergence of iterative projection methods for symmetric eigenvalue problems ⋮ Functions of rational Krylov space matrices and their decay properties ⋮ Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations ⋮ Generation of orthogonal rational functions by procedures for structured matrices ⋮ A Padé-based factorization-free algorithm for identifying the eigenvalues missed by a generalized symmetric eigensolver ⋮ Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations

Uses Software

• JDQR
• JDQZ
• IRAM

Cites Work

• Unnamed Item
• A rational Lanczos algorithm for model reduction
• A Krylov--Schur Algorithm for Large Eigenproblems
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
• Templates for the Solution of Algebraic Eigenvalue Problems
• On computing givens rotations reliably and efficiently
• An algorithm for numerical determination of the structure of a general matrix

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