The implicit application of a rational filter in the RKS method

DOI10.1007/BF02510361zbMath0890.65035MaRDI QIDQ1378473

Adhemar Bultheel, Karl Meerbergen, Gorik De Samblanx

Publication date: 6 July 1998

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

eigenvalueseigenvectorsrational filterrestarted Arnoldi methodrational Krylov subspace methodshift-invert

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (7)

An implicit filter for rational Krylov using core transformations ⋮ Compact Two-Sided Krylov Methods for Nonlinear Eigenvalue Problems ⋮ A Rational QZ Method ⋮ Using implicitly filtered RKS for generalised eigenvalue problems ⋮ Restrictions on implicit filtering techniques for orthogonal projection methods ⋮ Compact Rational Krylov Methods for Nonlinear Eigenvalue Problems ⋮ Generalized Rational Krylov Decompositions with an Application to Rational Approximation

Uses Software

• eigs
• JDQZ
• IRAM

Cites Work

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• Rational Krylov sequence methods for eigenvalue computation
• Complex shift and invert strategies for real matrices
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• The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices
• Implicitly restarted Arnoldi with purification for the shift-invert transformation
• How to Implement the Spectral Transformation
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Forward Instability of Tridiagonal QR
• Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
• A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
• A Jacobi--Davidson Iteration Method for Linear Eigenvalue Problems
• Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
• Forward Stability and Transmission of Shifts in the $QR$ Algorithm
• Matrix transformations for computing rightmost eigenvalues of large sparse non-symmetric eigenvalue problems
• On restarting the Arnoldi method for large nonsymmetric eigenvalue problems

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